1
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Wang H, Li W, Shi L, Chen G, Tu Z. Modeling and analysis of the effect of optimal virus control on the spread of HFMD. Sci Rep 2024; 14:6387. [PMID: 38493254 PMCID: PMC10944539 DOI: 10.1038/s41598-024-56839-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Accepted: 03/12/2024] [Indexed: 03/18/2024] Open
Abstract
A within-host and between-host hand, foot and mouth disease (HFMD) mathematical model is established and the affect of optimal control in its within-host part on HFMD transmission is studied. Through define two basic reproduction numbers, by using the fast-slow system analysis method of time scale, the global stabilities of the between-host (slow) system and within-host (fast) system are researched, respectively. An optimal control problem with drug-treatment control on coupled within-host and between-host HFMD model is formulated and analysed theoretically. Finally, the purposed optimal control measures are applied to the actual HFMD epidemic analysis in Zhejiang Province, China from April 1, 2021 to June 30, 2021. The numerical results show that the drug control strategies can reduce the virus load per capita and can effectively prevent large-scale outbreaks of HFMD.
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Affiliation(s)
- Hui Wang
- College of Nursing, Chongqing Three Gorges Medical College, Wanzhou, 404120, China.
| | - Weihua Li
- College of Nursing, Chongqing Three Gorges Medical College, Wanzhou, 404120, China
| | - Lei Shi
- School of Mathematics and Statistics, Guilin University of Technology, Guilin, 541004, China
| | - Gaofang Chen
- School of Mathematics and Statistics, Guilin University of Technology, Guilin, 541004, China
| | - Zhengwen Tu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China
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2
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Micuda AN, Anderson MR, Babayan I, Bolger E, Cantin L, Groth G, Pressman-Cyna R, Reed CZ, Rowe NJ, Shafiee M, Tam B, Vidal MC, Ye T, Martin RD. Exploring a targeted approach for public health capacity restrictions during COVID-19 using a new computational model. Infect Dis Model 2024; 9:234-244. [PMID: 38303993 PMCID: PMC10831812 DOI: 10.1016/j.idm.2024.01.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2023] [Revised: 12/17/2023] [Accepted: 01/06/2024] [Indexed: 02/03/2024] Open
Abstract
This work introduces the Queen's University Agent-Based Outbreak Outcome Model (QUABOOM). This tool is an agent-based Monte Carlo simulation for modelling epidemics and informing public health policy. We illustrate the use of the model by examining capacity restrictions during a lockdown. We find that public health measures should focus on the few locations where many people interact, such as grocery stores, rather than the many locations where few people interact, such as small businesses. We also discuss a case where the results of the simulation can be scaled to larger population sizes, thereby improving computational efficiency.
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Affiliation(s)
- Ashley N. Micuda
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
- Department of Medical Biophysics, Western University, London, ON, Canada
| | - Mark R. Anderson
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
| | - Irina Babayan
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
| | - Erin Bolger
- Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada
- Department of Biology, Queen's University, Kingston, ON, Canada
| | - Logan Cantin
- School of Computing, Queen's University, Kingston, ON, Canada
| | - Gillian Groth
- Department of Biomedical and Molecular Sciences, Queen's University, Kingston, ON, Canada
| | - Ry Pressman-Cyna
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
| | - Charlotte Z. Reed
- Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada
| | - Noah J. Rowe
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
| | - Mehdi Shafiee
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
- Department of Electrical and Computer Engineering, Nazarbayev University, Nur-Sultan, Kazakhstan
- Energetic Cosmos Laboratory, Nazarbayev University, Nur-Sultan, Kazakhstan
| | - Benjamin Tam
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
- Department of Physics, University of Oxford, Oxford, United Kingdom
| | - Marie C. Vidal
- Department of Physics, Stanford University, Stanford, CA, United States
| | - Tianai Ye
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
| | - Ryan D. Martin
- Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, ON, Canada
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3
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McKee J, Dallas T. Structural network characteristics affect epidemic severity and prediction in social contact networks. Infect Dis Model 2024; 9:204-213. [PMID: 38293687 PMCID: PMC10824764 DOI: 10.1016/j.idm.2023.12.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 11/14/2023] [Accepted: 12/27/2023] [Indexed: 02/01/2024] Open
Abstract
Understanding and mitigating epidemic spread in complex networks requires the measurement of structural network properties associated with epidemic risk. Classic measures of epidemic thresholds like the basic reproduction number (R0) have been adapted to account for the structure of social contact networks but still may be unable to capture epidemic potential relative to more recent measures based on spectral graph properties. Here, we explore the ability of R0 and the spectral radius of the social contact network to estimate epidemic susceptibility. To do so, we simulate epidemics on a series of constructed (small world, scale-free, and random networks) and a collection of over 700 empirical biological social contact networks. Further, we explore how other network properties are related to these two epidemic estimators (R0 and spectral radius) and mean infection prevalence in simulated epidemics. Overall, we find that network properties strongly influence epidemic dynamics and the subsequent utility of R0 and spectral radius as indicators of epidemic risk.
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Affiliation(s)
- Jae McKee
- Bioinnovation Program, Tulane University, New Orleans, LA, 70118, USA
- Department of Medicine, Tulane University School of Medicine, New Orleans, LA, 70112, USA
| | - Tad Dallas
- Department of Biological Sciences, University of South Carolina, Columbia, SC, 29208, USA
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4
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Ullah MS, Kamrujjaman M, Kabir KMA. Understanding the relationship between stay-at-home measures and vaccine shortages: a conventional, heterogeneous, and fractional dynamic approach. J Health Popul Nutr 2024; 43:32. [PMID: 38424608 DOI: 10.1186/s41043-024-00505-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 01/13/2024] [Indexed: 03/02/2024]
Abstract
In light of the global prevalence of a highly contagious respiratory disease, this study presents a novel approach to address the pressing and unanticipated issues by introducing a modified vaccination and lockdown-centered epidemic model. The rapid spread of the disease is attributed to viral transmissibility, the emergence of new strains (variants), lack of immunization, and human unawareness. This study aims to provide policymakers with crucial insights for making informed decisions regarding lockdown strategies, vaccine availability, and other control measures. The research adopts three types of models: deterministic, heterogeneous, and fractional-order dynamics, on both theoretical and numerical approaches. The heterogeneous network considers varying connectivity and interaction patterns among individuals, while the ABC fractional-order derivatives analyze the impact of integer-order control in different semi-groups. An extensive theoretical analysis is conducted to validate the proposed model. A comprehensive numerical investigation encompasses deterministic, stochastic, and ABC fractional-order derivatives, considering the combined effects of an effective vaccination program and non-pharmaceutical interventions, such as lockdowns and shutdowns. The findings of this research are expected to be valuable for policymakers in different countries, helping them implement dynamic strategies to control and eradicate the epidemic effectively.
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Affiliation(s)
| | | | - K M Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
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5
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Pisaneschi G, Tarani M, Di Donato G, Landi A, Laurino M, Manfredi P. Optimal social distancing in epidemic control: cost prioritization, adherence and insights into preparedness principles. Sci Rep 2024; 14:4365. [PMID: 38388727 PMCID: PMC10883963 DOI: 10.1038/s41598-024-54955-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 02/19/2024] [Indexed: 02/24/2024] Open
Abstract
The COVID-19 pandemic experience has highlighted the importance of developing general control principles to inform future pandemic preparedness based on the tension between the different control options, ranging from elimination to mitigation, and related costs. Similarly, during the COVID-19 pandemic, social distancing has been confirmed to be the critical response tool until vaccines become available. Open-loop optimal control of a transmission model for COVID-19 in one of its most aggressive outbreaks is used to identify the best social distancing policies aimed at balancing the direct epidemiological costs of a threatening epidemic with its indirect (i.e., societal level) costs arising from enduring control measures. In particular, we analyse how optimal social distancing varies according to three key policy factors, namely, the degree of prioritization of indirect costs, the adherence to control measures, and the timeliness of intervention. As the prioritization of indirect costs increases, (i) the corresponding optimal distancing policy suddenly switches from elimination to suppression and, finally, to mitigation; (ii) the "effective" mitigation region-where hospitals' overwhelming is prevented-is dramatically narrow and shows multiple control waves; and (iii) a delicate balance emerges, whereby low adherence and lack of timeliness inevitably force ineffective mitigation as the only accessible policy option. The present results show the importance of open-loop optimal control, which is traditionally absent in public health preparedness, for studying the suppression-mitigation trade-off and supplying robust preparedness guidelines.
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Affiliation(s)
- Giulio Pisaneschi
- Department of Information Engineering, University of Pisa, Pisa, Italy
| | - Matteo Tarani
- Department of Information Engineering, University of Pisa, Pisa, Italy
| | | | - Alberto Landi
- Department of Information Engineering, University of Pisa, Pisa, Italy
| | - Marco Laurino
- Institute of Clinical Physiology, National Research Council, Pisa, Italy
| | - Piero Manfredi
- Department of Economics and Management, University of Pisa, Pisa, Italy.
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6
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Jamil S, Bariq A, Farman M, Nisar KS, Akgül A, Saleem MU. Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator. Sci Rep 2024; 14:2175. [PMID: 38272984 DOI: 10.1038/s41598-023-51121-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 12/31/2023] [Indexed: 01/27/2024] Open
Abstract
Respiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.
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Affiliation(s)
- Saba Jamil
- Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
| | - Abdul Bariq
- Department of Mathematics, Laghman University, Mehtarlam, 2701, Laghman, Afghanistan.
| | - Muhammad Farman
- Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
- Department of Mathematics, Faculty of Arts and Sciences, Near East University, Mersin, Turkey
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia
| | - Ali Akgül
- Department of Mathematics, Faculty of Arts and Sciences, Near East University, Mersin, Turkey
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
- Department of Mathematics, Art and Science Faculty, Siirt University, 56100, Siirt, Turkey
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7
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Gao C, Zhang T, Liao Y, Wang Y, Jiao H, Wu M, Cui Q, Wang K, Wang L. Modelling of tuberculosis dynamics incorporating indirect transmission of contaminated environment and infectivity of smear-negative individuals: a case study for Xinjiang, China. Acta Trop 2024:107130. [PMID: 38278313 DOI: 10.1016/j.actatropica.2024.107130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Revised: 01/21/2024] [Accepted: 01/22/2024] [Indexed: 01/28/2024]
Abstract
Xinjiang has been one of the high incidence areas of pulmonary tuberculosis (PTB) in China. Besides being infected by direct contacting with active PTB individuals (direct infection), the susceptible would be infected because of the exposure to the environment contaminated by Mycobacterium tuberculosis (indirect infection). Active PTB individuals include not only the smear-positive PTB (PTB+) but also the smear-negative PTB (PTB-) who are infectious due to their ability to release tiny Mycobacterium tuberculosis particles even in the absence of visible Mycobacterium tuberculosis in sputum. By taking account of direct/indirect infection and the difference between PTB+ and PTB- individuals in transmission capability, a periodic dynamical PTB transmission model is proposed. The model is fitted to the newly monthly PTB+ and PTB- cases in Xinjiang from 2008 to 2017 by Markov Chain Monte Carlo algorithm. Moreover, global sensitivity analysis is constructed to address the uncertainty of some key parameters by using Latin hypercube sampling and partial rank correlation coefficient methods. Basic reproduction number R0 for PTB transmission in Xinjiang is estimated to be 2.447 (95% CrI:(1.203, 3.844)), indicating that PTB has been prevalent in Xinjiang over the study period. Our results suggest that reducing the direct/indirect transmission rates, early screening, isolating and treating the latent, PTB+ and PTB- individuals, and enhancing the clearance of Mycobacterium tuberculosis in the environment could more effectively control PTB transmission in Xinjiang. The model fits the reported PTB data well and achieves acceptable prediction accuracy. We believe that our model can provide heuristic support for controlling PTB transmission in Xinjiang.
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Affiliation(s)
- Chunjie Gao
- College of Public Health, Xinjiang Medical University, Urumqi 830017, China.
| | - Tao Zhang
- College of Public Health, Xinjiang Medical University, Urumqi 830017, China.
| | - Ying Liao
- Department of Disease Control, Liangping District Center for Disease Prevention and Control, Chongqing 405200,China.
| | - Yingdan Wang
- Department of Medical records, Yanan University Xianyang Hospital, Xianyang 712000, China.
| | - Haiyan Jiao
- Medical Department, Linxia Maternal and Child Health Hospital, Gansu 731100, China.
| | - Mengjuan Wu
- College of Public Health, Xinjiang Medical University, Urumqi 830017, China.
| | - Qianqian Cui
- School of Mathematics and Statistics, Ningxia University, Ningxia 750021, China.
| | - Kai Wang
- Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China.
| | - Lei Wang
- Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China.
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8
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Hu X, Hu Z, Xu T, Zhang K, Lu HH, Zhao J, Boerwinkle E, Jin L, Xiong M. Equilibrium points and their stability of COVID-19 in US. Sci Rep 2024; 14:1628. [PMID: 38238368 PMCID: PMC10796349 DOI: 10.1038/s41598-024-51729-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 01/09/2024] [Indexed: 01/22/2024] Open
Abstract
This study aims to develop an advanced mathematic model and investigate when and how will the COVID-19 in the US be evolved to endemic. We employed a nonlinear ordinary differential equations-based model to simulate COVID-19 transmission dynamics, factoring in vaccination efforts. Multi-stability analysis was performed on daily new infection data from January 12, 2021 to December 12, 2022 across 50 states in the US. Key indices such as eigenvalues and the basic reproduction number were utilized to evaluate stability and investigate how the pandemic COVD-19 will evolve to endemic in the US. The transmissional, recovery, vaccination rates, vaccination effectiveness, eigenvalues and reproduction numbers ([Formula: see text] and [Formula: see text]) in the endemic equilibrium point were estimated. The stability attractor regions for these parameters were identified and ranked. Our multi-stability analysis revealed that while the endemic equilibrium points in the 50 states remain unstable, there is a significant trend towards stable endemicity in the US. The study's stability analysis, coupled with observed epidemiological waves in the US, suggested that the COVID-19 pandemic may not conclude with the virus's eradication. Nevertheless, the virus is gradually becoming endemic. Effectively strategizing vaccine distribution is pivotal for this transition.
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Affiliation(s)
- Xiaoxi Hu
- State Key Laboratory of Genetic Engineering and Innovation Center of Genetics and Development, School of Life Sciences, Fudan University, Shanghai, China
| | - Zixin Hu
- State Key Laboratory of Genetic Engineering and Innovation Center of Genetics and Development, School of Life Sciences, Fudan University, Shanghai, China
- Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, China
| | - Tao Xu
- Department of Epidemiology, University of Florida, Gainesville, FL, 32611, USA
| | - Kai Zhang
- Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, Rensselaer, NY, 12144, USA
| | | | - Jinying Zhao
- Department of Epidemiology, University of Florida, Gainesville, FL, 32611, USA
| | - Eric Boerwinkle
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX, 77030, USA
| | - Li Jin
- State Key Laboratory of Genetic Engineering and Innovation Center of Genetics and Development, School of Life Sciences, Fudan University, Shanghai, China
| | - Momiao Xiong
- Department of Biostatistics and Data Science, School of Public Health, The University of Texas Health Science Center at Houston, P.O. Box 20186, Houston, TX, 77030, USA.
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9
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Alòs J, Ansótegui C, Dotu I, García-Herranz M, Pastells P, Torres E. ePyDGGA: automatic configuration for fitting epidemic curves. Sci Rep 2024; 14:784. [PMID: 38191771 PMCID: PMC10774272 DOI: 10.1038/s41598-023-43958-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 09/30/2023] [Indexed: 01/10/2024] Open
Abstract
Many epidemiological models and algorithms are used to fit the parameters of a given epidemic curve. On many occasions, fitting algorithms are interleaved with the actual epidemic models, which yields combinations of model-parameters that are hard to compare among themselves. Here, we provide a model-agnostic framework for epidemic parameter fitting that can (fairly) compare different epidemic models without jeopardizing the quality of the fitted parameters. Briefly, we have developed a Python framework that expects a Python function (epidemic model) and epidemic data and performs parameter fitting using automatic configuration. Our framework is capable of fitting parameters for any type of epidemic model, as long as it is provided as a Python function (or even in a different programming language). Moreover, we provide the code for different types of models, as well as the implementation of 4 concrete models with data to fit them. Documentation, code and examples can be found at https://ulog.udl.cat/static/doc/epidemic-gga/html/index.html .
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Affiliation(s)
- Josep Alòs
- Logic and Optimization Group, University of Lleida, Lleida, Spain.
| | - Carlos Ansótegui
- Logic and Optimization Group, University of Lleida, Lleida, Spain.
| | | | | | | | - Eduard Torres
- Logic and Optimization Group, University of Lleida, Lleida, Spain
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10
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Li W, Cai S, Zhai X, Ou J, Zheng K, Wei F, Mao X. Transmission dynamics of symptom-dependent HIV/AIDS models. Math Biosci Eng 2024; 21:1819-1843. [PMID: 38454662 DOI: 10.3934/mbe.2024079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/09/2024]
Abstract
In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0^s $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.
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Affiliation(s)
- Wenshuang Li
- School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
| | - Shaojian Cai
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Xuanpei Zhai
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Jianming Ou
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Kuicheng Zheng
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Fengying Wei
- School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
- Center for Applied Mathematics of Fujian Province, Fuzhou University, Fuzhou 350116, Fujian, China
- Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou University, Fuzhou 350116, Fujian, China
| | - Xuerong Mao
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
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11
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Das S, Srivastava PK, Biswas P. Exploring Hopf-bifurcations and endemic bubbles in a tuberculosis model with behavioral changes and treatment saturation. Chaos 2024; 34:013126. [PMID: 38252782 DOI: 10.1063/5.0179351] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Accepted: 12/22/2023] [Indexed: 01/24/2024]
Abstract
To manage risks and minimize the transmission of contagious diseases, individuals may reduce their contact with each other and take other precautions as much as possible in their daily lives and workplaces. As a result, the transmission of the infection reduces due to the behavioral changes. These behavioral changes are incorporated into models by introducing saturation in disease incidence. In this article, we propose and analyze a tuberculosis model that incorporates saturated exogenous reinfection and treatment. The stability analysis of the model's steady states is rigorously examined. We observe that the disease-free equilibrium point and the endemic equilibrium point (EEP) are globally asymptotically stable if the basic reproduction number (R0) is less than 1 and greater than 1, respectively, only when exogenous reinfection is not present (p=0) and when treatment is available for all (ω=0). However, even when R0 is less than 1, tuberculosis may persist at a specific level in the presence of exogenous reinfection and treatment saturation, leading to a backward bifurcation in the system. The existence and direction of Hopf-bifurcations are also discussed. Furthermore, we numerically validate our analytical results using different parameter sets. In the numerical examples, we study Hopf-bifurcations for parameters such as β, p, α, and ω. In one example, we observe that increasing β leads to the loss of stability of the unique EEP through a forward Hopf-bifurcation. If β is further increased, the unique EEP restores its stability, and the bifurcation diagram exhibits an interesting structure known as an endemic bubble. The existence of an endemic bubble for the saturation constant ω is also observed.
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Affiliation(s)
- Saduri Das
- National Institute of Technology Silchar, Silchar 788010, Assam, India
| | | | - Pankaj Biswas
- National Institute of Technology Silchar, Silchar 788010, Assam, India
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12
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Thakkar K, Spinardi J, Kyaw MH, Yang J, Mendoza CF, Ozbilgili E, Taysi B, Dodd J, Yarnoff B, Oh HM. Modelling the Potential Public Health Impact of Different COVID-19 Vaccination Strategies with an Adapted Vaccine in Singapore. Expert Rev Vaccines 2024; 23:16-26. [PMID: 38047434 DOI: 10.1080/14760584.2023.2290931] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2023] [Accepted: 11/30/2023] [Indexed: 12/05/2023]
Abstract
BACKGROUND Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causing COVID-19 has been a dynamically changing virus, requiring the development of adapted vaccines. This study estimated the potential public health impact alternative vaccination strategies for COVID-19 in Singapore. RESEARCH DESIGN AND METHODS The outcomes of alternative vaccination strategies with a future adapted vaccine were estimated using a combined Markov decision tree model. The population was stratified by high- and standard-risk. Using age-specific inputs informed by local surveillance data and published sources, the model estimated health (case numbers, hospitalizations, and deaths) and economic (medical costs and productivity losses) outcomes in different age and risk subpopulations. RESULTS Booster vaccination in only the elderly and high-risk subpopulation was estimated to avert 278,614 cases 21,558 hospitalizations, 239 deaths, Singapore dollars (SGD) 277 million in direct medical costs, and SGD 684 million in indirect medical costs. These benefits increased as vaccination was expanded to other subpopulations. Increasing the booster vaccination coverage to 75% of the standard-risk population averted more deaths (3%), hospitalizations (29%), infections (145%), direct costs (90%), and indirect costs (192%) compared to the base case. CONCLUSIONS Broader vaccination strategies using an adapted booster vaccine could have substantial public health and economic impact in Singapore.
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Affiliation(s)
| | - Julia Spinardi
- Medical and Scientific Affairs, Pfizer Inc, New York, NY, USA
| | - Moe H Kyaw
- Medical and Scientific Affairs, Pfizer Inc, New York, NY, USA
| | - Jingyan Yang
- Value and Evidence, Pfizer Inc, New York, NY, USA
| | | | | | - Bulent Taysi
- Asia Medical Affairs, Pfizer Inc, New York, NY, USA
| | - Josie Dodd
- Modeling and Simulation, Evidera Inc, Bethesda, MD, USA
| | - Ben Yarnoff
- Modeling and Simulation, Evidera Inc, Bethesda, MD, USA
| | - Helen M Oh
- Department of Infectious Disease, Changi General Hospital, Simei, Singapore
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13
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Obeid M, Abd El Salam MA, Younis JA. Operational matrix-based technique treating mixed type fractional differential equations via shifted fifth-kind Chebyshev polynomials. Applied Mathematics in Science and Engineering 2023; 31. [DOI: 10.1080/27690911.2023.2187388] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 02/28/2023] [Indexed: 09/02/2023]
Affiliation(s)
- Mohamed Obeid
- Department of Mathematics, Faculty of Science, Al Azhar University, Cairo, Egypt
| | - Mohamed A. Abd El Salam
- Department of Mathematics, Faculty of Science, Al Azhar University, Cairo, Egypt
- Basic Science Department, October High Institute for Engineering and Technology, Giza, Egypt
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14
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Guttieres D, Diepvens C, Decouttere C, Vandaele N. Modeling Supply and Demand Dynamics of Vaccines against Epidemic-Prone Pathogens: Case Study of Ebola Virus Disease. Vaccines (Basel) 2023; 12:24. [PMID: 38250837 PMCID: PMC10819028 DOI: 10.3390/vaccines12010024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2023] [Revised: 12/13/2023] [Accepted: 12/22/2023] [Indexed: 01/23/2024] Open
Abstract
Health emergencies caused by epidemic-prone pathogens (EPPs) have increased exponentially in recent decades. Although vaccines have proven beneficial, they are unavailable for many pathogens. Furthermore, achieving timely and equitable access to vaccines against EPPs is not trivial. It requires decision-makers to capture numerous interrelated factors across temporal and spatial scales, with significant uncertainties, variability, delays, and feedback loops that give rise to dynamic and unexpected behavior. Therefore, despite progress in filling R&D gaps, the path to licensure and the long-term viability of vaccines against EPPs continues to be unclear. This paper presents a quantitative system dynamics modeling framework to evaluate the long-term sustainability of vaccine supply under different vaccination strategies. Data from both literature and 50 expert interviews are used to model the supply and demand of a prototypical Ebolavirus Zaire (EBOV) vaccine. Specifically, the case study evaluates dynamics associated with proactive vaccination ahead of an outbreak of similar magnitude as the 2018-2020 epidemic in North Kivu, Democratic Republic of the Congo. The scenarios presented demonstrate how uncertainties (e.g., duration of vaccine-induced protection) and design criteria (e.g., priority geographies and groups, target coverage, frequency of boosters) lead to important tradeoffs across policy aims, public health outcomes, and feasibility (e.g., technical, operational, financial). With sufficient context and data, the framework provides a foundation to apply the model to a broad range of additional geographies and priority pathogens. Furthermore, the ability to identify leverage points for long-term preparedness offers directions for further research.
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Affiliation(s)
- Donovan Guttieres
- Access-to-Medicines Research Centre, Faculty of Economics & Business, KU Leuven, 3000 Leuven, Belgium; (C.D.); (C.D.); (N.V.)
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15
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Alonso D, Vallès X. A potential transition from a concentrated to a generalized HIV epidemic: the case of Madagascar. Infect Dis Poverty 2023; 12:112. [PMID: 38057918 DOI: 10.1186/s40249-023-01164-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 11/20/2023] [Indexed: 12/08/2023] Open
Abstract
BACKGROUND HIV expansion is controlled by a range of interrelated factors, including the natural history of HIV infection and socio-economical and structural factors. However, how they dynamically interact in particular contexts to drive a transition from concentrated HIV epidemics in vulnerable groups to generalized epidemics is poorly understood. We aim to explore these mechanisms, using Madagascar as a case-study. METHODS We developed a compartmental dynamic model using available data from Madagascar, a country with a contrasting concentrated epidemic, to explore the interaction between these factors with special consideration of commercial and transactional sex as HIV-infection drivers. RESULTS The model predicts sigmoidal-like prevalence curves with turning points within years 2020-2022, and prevalence reaching stabilization by 2033 within 9 to 24% in the studied (10 out of 11) cities, similar to high-prevalence regions in Southern Africa. The late/slow introduction of HIV and circumcision, a widespread traditional practice in Madagascar, could have slowed down HIV propagation, but, given the key interplay between risky behaviors associated to young women and acute infections prevalence, mediated by transactional sex, the protective effect of circumcision is currently insufficient to contain the expansion of the disease in Madagascar. CONCLUSIONS These results suggest that Madagascar may be experiencing a silent transition from a concentrated to a generalized HIV epidemic. This case-study model could help to understand how this HIV epidemic transition occurs.
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Affiliation(s)
- David Alonso
- Computational and Theoretical Ecology, Spanish Council for Scientific Research (CEAB-CSI)C, C/Access Cala Francesc, 14, 17300, Blanes, Spain
| | - Xavier Vallès
- International Health Program (PROSICS), North Metropolitan Health Area From Barcelona, Hospital Universitari Germans Trias i Pujol, Passatge dels Encants, s/n, 08914, Badalona, Catalonia, Spain.
- Institut d'Investigació en Ciències de la Salut Germans Trias i Pujol, C/Canyet s/n, 08916, Badalona, Spain.
- Fundació Lluita contra les Infeccions, C/Canyet s/n, 08916, Badalona, Spain.
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16
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Xue L, Sun Y, Ren X, Sun W. Modelling the transmission dynamics and optimal control strategies for HIV infection in China. J Biol Dyn 2023; 17:2174275. [PMID: 36787262 DOI: 10.1080/17513758.2023.2174275] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 12/08/2022] [Indexed: 06/18/2023]
Abstract
In order to end the AIDS epidemic by 2030 that was put forward by the Joint United Nations Programme on HIV/AIDS in 2014, China needs to take more effective measures to achieve the three 90% goals (90-90-90). We establish a compartmental model to study the dynamics of HIV transmission with control strategies. The analytical results show the existence and stability of the disease-free equilibrium and endemic equilibrium. An optimal control model is constructed to evaluate the impacts of control measures. The simulation results show that the optimal control strategy proposed in this work can eradicate AIDS by 2030. The cost-effectiveness analysis indicates that the cost of the control strategy that combines screening for latent individuals and enhancing education for unaware infected individuals is the lowest. Our findings can provide guidance for public health authorities on effective mitigation strategies to achieve the goals proposed by the United Nations Program on HIV/AIDS.
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Affiliation(s)
- Ling Xue
- College of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of China
| | - Yuanmei Sun
- College of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of China
| | - Xue Ren
- College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, People's Republic of China
| | - Wei Sun
- College of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of China
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17
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Lee B, Song H, Apio C, Han K, Park J, Liu Z, Xuwen H, Park T. An analysis of the waning effect of COVID-19 vaccinations. Genomics Inform 2023; 21:e50. [PMID: 38224717 PMCID: PMC10788359 DOI: 10.5808/gi.23088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2023] [Revised: 12/12/2023] [Accepted: 12/12/2023] [Indexed: 01/17/2024] Open
Abstract
Vaccine development is one of the key efforts to control the spread of coronavirus disease 2019 (COVID-19). However, it has become apparent that the immunity acquired through vaccination is not permanent, known as the waning effect. Therefore, monitoring the proportion of the population with immunity is essential to improve the forecasting of future waves of the pandemic. Despite this, the impact of the waning effect on forecasting accuracies has not been extensively studied. We proposed a method for the estimation of the effective immunity (EI) rate which represents the waning effect by integrating the second and booster doses of COVID-19 vaccines. The EI rate, with different periods to the onset of the waning effect, was incorporated into three statistical models and two machine learning models. Stringency Index, omicron variant BA.5 rate (BA.5 rate), booster shot rate (BSR), and the EI rate were used as covariates and the best covariate combination was selected using prediction error. Among the prediction results, Generalized Additive Model showed the best improvement (decreasing 86% test error) with the EI rate. Furthermore, we confirmed that South Korea's decision to recommend booster shots after 90 days is reasonable since the waning effect onsets 90 days after the last dose of vaccine which improves the prediction of confirmed cases and deaths. Substituting BSR with EI rate in statistical models not only results in better predictions but also makes it possible to forecast a potential wave and help the local community react proactively to a rapid increase in confirmed cases.
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Affiliation(s)
- Bogyeom Lee
- Department of Industrial Engineering, Seoul National University, Seoul 08826, Korea
| | - Hanbyul Song
- Interdisciplinary Program of Bioinformatics, Seoul National University, Seoul 08826, Korea
| | - Catherine Apio
- Interdisciplinary Program of Bioinformatics, Seoul National University, Seoul 08826, Korea
| | - Kyulhee Han
- Interdisciplinary Program of Bioinformatics, Seoul National University, Seoul 08826, Korea
| | - Jiwon Park
- Interdisciplinary Program of Bioinformatics, Seoul National University, Seoul 08826, Korea
| | - Zhe Liu
- Interdisciplinary Program of Bioinformatics, Seoul National University, Seoul 08826, Korea
| | - Hu Xuwen
- Department of Statistics, Seoul National University, Seoul 08826, Korea
| | - Taesung Park
- Department of Statistics, Seoul National University, Seoul 08826, Korea
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18
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Grieve R, Yang Y, Abbott S, Babu GR, Bhattacharyya M, Dean N, Evans S, Jewell N, Langan SM, Lee W, Molenberghs G, Smeeth L, Williamson E, Mukherjee B. The importance of investing in data, models, experiments, team science, and public trust to help policymakers prepare for the next pandemic. PLOS Glob Public Health 2023; 3:e0002601. [PMID: 38032861 PMCID: PMC10688710 DOI: 10.1371/journal.pgph.0002601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/02/2023]
Abstract
The COVID-19 pandemic has brought about valuable insights regarding models, data, and experiments. In this narrative review, we summarised the existing literature on these three themes, exploring the challenges of providing forecasts, the requirement for real-time linkage of health-related datasets, and the role of 'experimentation' in evaluating interventions. This literature review encourages us to broaden our perspective for the future, acknowledging the significance of investing in models, data, and experimentation, but also to invest in areas that are conceptually more abstract: the value of 'team science', the need for public trust in science, and in establishing processes for using science in policy. Policy-makers rely on model forecasts early in a pandemic when there is little data, and it is vital to communicate the assumptions, limitations, and uncertainties (theme 1). Linked routine data can provide critical information, for example, in establishing risk factors for adverse outcomes but are often not available quickly enough to make a real-time impact. The interoperability of data resources internationally is required to facilitate sharing across jurisdictions (theme 2). Randomised controlled trials (RCTs) provided timely evidence on the efficacy and safety of vaccinations and pharmaceuticals but were largely conducted in higher income countries, restricting generalisability to low- and middle-income countries (LMIC). Trials for non-pharmaceutical interventions (NPIs) were almost non-existent which was a missed opportunity (theme 3). Building on these themes from the narrative review, we underscore the importance of three other areas that need investment for effective evidence-driven policy-making. The COVID-19 response relied on strong multidisciplinary research infrastructures, but funders and academic institutions need to do more to incentivise team science (4). To enhance public trust in the use of scientific evidence for policy, researchers and policy-makers must work together to clearly communicate uncertainties in current evidence and any need to change policy as evidence evolves (5). Timely policy decisions require an established two-way process between scientists and policy makers to make the best use of evidence (6). For effective preparedness against future pandemics, it is essential to establish models, data, and experiments as fundamental pillars, complemented by efforts in planning and investment towards team science, public trust, and evidence-based policy-making across international communities. The paper concludes with a 'call to actions' for both policy-makers and researchers.
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Affiliation(s)
- Richard Grieve
- Centre for Data and Statistical Science for Health (DASH), London School of Hygiene and Tropical Medicine, London, United Kingdom
- Department of Health Services Research and Policy, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Youqi Yang
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Sam Abbott
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Giridhara R. Babu
- Indian Institute of Public Health, Public Health Foundation of India, Bengaluru, India
| | | | - Natalie Dean
- Department of Biostatistics & Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, Georgia, United States of America
| | - Stephen Evans
- Centre for Data and Statistical Science for Health (DASH), London School of Hygiene and Tropical Medicine, London, United Kingdom
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Nicholas Jewell
- Centre for Data and Statistical Science for Health (DASH), London School of Hygiene and Tropical Medicine, London, United Kingdom
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Sinéad M. Langan
- Department of Non-communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Woojoo Lee
- Department of Public Health Sciences, Graduate School of Public Health, Seoul National University, Seoul, Republic of Korea
| | - Geert Molenberghs
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Universiteit Hasselt & KU Leuven, Hasselt, Belgium
| | - Liam Smeeth
- Department of Non-communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Elizabeth Williamson
- Centre for Data and Statistical Science for Health (DASH), London School of Hygiene and Tropical Medicine, London, United Kingdom
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Bhramar Mukherjee
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, United States of America
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19
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Liu L, Wang X, Li Y. Mathematical analysis and optimal control of an epidemic model with vaccination and different infectivity. Math Biosci Eng 2023; 20:20914-20938. [PMID: 38124581 DOI: 10.3934/mbe.2023925] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2023]
Abstract
This paper aims to explore the complex dynamics and impact of vaccinations on controlling epidemic outbreaks. An epidemic transmission model which considers vaccinations and two different infection statuses with different infectivity is developed. In terms of a dynamic analysis, we calculate the basic reproduction number and control reproduction number and discuss the stability of the disease-free equilibrium. Additionally, a numerical simulation is performed to explore the effects of vaccination rate, immune waning rate and vaccine ineffective rate on the epidemic transmission. Finally, a sensitivity analysis revealed three factors that can influence the threshold: transmission rate, vaccination rate, and the hospitalized rate. In terms of optimal control, the following three time-related control variables are introduced to reconstruct the corresponding control problem: reducing social distance, enhancing vaccination rates, and enhancing the hospitalized rates. Moreover, the characteristic expression of optimal control problem. Four different control combinations are designed, and comparative studies on control effectiveness and cost effectiveness are conducted by numerical simulations. The results showed that Strategy C (including all the three controls) is the most effective strategy to reduce the number of symptomatic infections and Strategy A (including reducing social distance and enhancing vaccination rate) is the most cost-effective among the three strategies.
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Affiliation(s)
- Lili Liu
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
| | - Xi Wang
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
| | - Yazhi Li
- School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun 558000, China
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20
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Dano LB, Koya PR, Keno TD. Fractional optimal control strategies for hepatitis B virus infection with cost-effectiveness analysis. Sci Rep 2023; 13:19514. [PMID: 37945661 PMCID: PMC10636208 DOI: 10.1038/s41598-023-46849-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Accepted: 11/06/2023] [Indexed: 11/12/2023] Open
Abstract
Hepatitis B disease is a communicable disease that is caused by the hepatitis B virus and has become a significant health problem in the world. It is a contagious disease that is transmittable from person to person either horizontally or vertically. This current study is aimed at sensitivity analysis and optimal control strategies for a fractional hepatitis B epidemic model with a saturated incidence rate in the sense of the Caputo order fractional derivative approach. Fundamental properties of the proposed fractional order model are obtained and discussed. A detailed analysis of disease-free equilibrium and endemic equilibrium points is given by applying fractional calculus theory, which is a generalized version of classical calculus. Sensitivity indexes are calculated for the classical order model. Illustrative graphics that show the dependence of the sensitivity index on fractional order derivative for [Formula: see text] are provided. Based on the results of the sensitivity analysis and using Pontryagin's Maximum Principle, optimal control strategies for preventing hepatitis B infection with vaccination and treatment are considered. Fractional Euler's method is used to carry out the numerical simulation for the proposed fractional optimal control system and the obtained results are analyzed. The results of the analysis reveal that hepatitis B disease can be prevented if necessary precautionary is taken or effective vaccination and treatment control measures are applied. The analysis of cost-effectiveness is also conducted and discussed.
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21
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Chen C, Zhou Y, Ye Z. Stability and optimal control of a cytokine-enhanced general HIV infection model with antibody immune response and CTLs immune response. Comput Methods Biomech Biomed Engin 2023:1-32. [PMID: 37933845 DOI: 10.1080/10255842.2023.2275248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2023] [Accepted: 10/17/2023] [Indexed: 11/08/2023]
Abstract
In this article, a cytokine-enhanced viral infection model with cytotoxic T lymphocytes (CTLs) immune response and antibody immune response is proposed and analyzed. The model contains six compartments: uninfected CD4+T cells, infected CD4+T cells, inflammatory cytokines, viruses, CTLs and antibodies. Different from the previous works, this model not only considers virus-to-cell transmission and cell-to-cell transmission, but also includes a new infection mode, namely cytokine-enhanced viral infection. The incidence rates of the healthy CD4+T cells with viruses, infected cells and inflammatory cytokines are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. Firstly, we prove that all the solutions of the model are nonnegative and uniformly bounded. Then, five key parameters with strong biological significance, namely the virus basic reproduction number R0, CTLs immune response reproduction number R1, antibody immune response reproductive number R2, CTLs immune competitive reproductive number R3 and antibody immune competitive reproductive number R4 are derived. Then, by using Lyapunov's method and LaSalle's invariance principle, we have shown the global stability of each equilibrium. In addition, the numerical simulation results also show that the theoretical results are correct. Finally, we formulate an optimal control problem and solve it using Pontryagins Maximum Principle and an efficient iterative numerical methods. The results of our numerical simulation show that it is very important to control the infection between viruses and cells and between cells and inflammatory cytokines for controlling HIV.
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Affiliation(s)
- Chong Chen
- School of Mathematics and Statistics, Central South University, Changsha, China
| | - Yinggao Zhou
- School of Mathematics and Statistics, Central South University, Changsha, China
| | - Zhijian Ye
- School of Mathematics and Statistics, Central South University, Changsha, China
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22
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Olayiwola MO, Alaje AI, Olarewaju AY, Adedokun KA. A caputo fractional order epidemic model for evaluating the effectiveness of high-risk quarantine and vaccination strategies on the spread of COVID-19. Healthc Anal (N Y) 2023; 3:100179. [PMID: 37101804 PMCID: PMC10118058 DOI: 10.1016/j.health.2023.100179] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Revised: 04/15/2023] [Accepted: 04/15/2023] [Indexed: 04/28/2023]
Abstract
The recent global Coronavirus disease (COVID-19) threat to the human race requires research on preventing its reemergence without affecting socio-economic factors. This study proposes a fractional-order mathematical model to analyze the impact of high-risk quarantine and vaccination on COVID-19 transmission. The proposed model is used to analyze real-life COVID-19 data to develop and analyze the solutions and their feasibilities. Numerical simulations study the high-risk quarantine and vaccination strategies and show that both strategies effectively reduce the virus prevalence, but their combined application is more effective. We also demonstrate that their effectiveness varies with the volatile rate of change in the system's distribution. The results are analyzed using Caputo fractional order and presented graphically and extensively analyzed to highlight potent ways of curbing the virus.
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23
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Adeyemo S, Sangotola A, Korosteleva O. Modeling Transmission Dynamics of Tuberculosis-HIV Co-Infection in South Africa. Epidemiologia (Basel) 2023; 4:408-419. [PMID: 37873885 PMCID: PMC10594517 DOI: 10.3390/epidemiologia4040036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2023] [Revised: 10/07/2023] [Accepted: 10/09/2023] [Indexed: 10/25/2023] Open
Abstract
South Africa has the highest number of people living with the human immunodeficiency virus (HIV) in the world, accounting for nearly one in five people living with HIV globally. As of 2021, 8 million people in South Africa were infected with HIV, which is 13% of the country's total population. Approximately 450,000 people in the country develop tuberculosis (TB) disease every year, and 270,000 of those are HIV positive. This suggests that being HIV positive significantly increases one's susceptibility to TB, accelerating the spread of the epidemic. To better understand the disease burden at the population level, a Susceptible-Infected-Recovered-Dead (SIRD) TB-HIV co-infection epidemic model is presented. Parameter values are estimated using the method of moments. The disease-free equilibrium and basic reproduction number of the model are also obtained. Finally, numeric simulations are carried out for a 30-year period to give insights into the transmission dynamics of the co-infection.
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Affiliation(s)
- Simeon Adeyemo
- Department of Mathematics and Statistics, California State University, Long Beach, CA 90840, USA;
| | - Adekunle Sangotola
- Department of Physical Sciences, Bells University of Technology, Ota 112212, Ogun, Nigeria;
| | - Olga Korosteleva
- Department of Mathematics and Statistics, California State University, Long Beach, CA 90840, USA;
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24
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McCarthy ML, Wallace DI. Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever. Math Biosci Eng 2023; 20:18916-18938. [PMID: 38052583 DOI: 10.3934/mbe.2023837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
In some regions of the Americas, domestic dogs are the host for the tick vector Rhipicephalus sanguineus, and spread the tick-borne pathogen Rickettsia rickettsii, which causes Rocky Mountain Spotted Fever (RMSF) in humans. Interventions are carried out against the vector via dog collars and acaricidal wall treatments. This paper investigates the optimal control of acaricidal wall treatments, using a prior model for populations and disease transmission developed for this particular vector, host, and pathogen. It is modified with a death term during questing stages reflecting the cost of control and level of coverage. In the presence of the control, the percentage of dogs and ticks infected with Ri. rickettsii decreases in a short period and remains suppressed for a longer period, including after treatment is discontinued. Risk of RMSF infection declines by 90% during this time. In the absence of re-application, infected tick and dog populations rebound, indicating the eventual need for repeated treatment.
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Affiliation(s)
- Maeve L McCarthy
- Department of Mathematics & Statistics, Murray State University, 203A Industry & Technology, Murray KY 42071, USA
| | - Dorothy I Wallace
- Department of Mathematics, Dartmouth College, 27 N. Main Street, 6188 Kemeny Hall, Hanover, NH 03755-3551, USA
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AbuAli N, Khan MB, Sabir Z. A computational stochastic procedure for solving the epidemic breathing transmission system. Sci Rep 2023; 13:16220. [PMID: 37758765 PMCID: PMC10533895 DOI: 10.1038/s41598-023-43324-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Accepted: 09/22/2023] [Indexed: 09/29/2023] Open
Abstract
This work provides numerical simulations of the nonlinear breathing transmission epidemic system using the proposed stochastic scale conjugate gradient neural networks (SCGGNNs) procedure. The mathematical model categorizes the breathing transmission epidemic model into four dynamics based on a nonlinear stiff ordinary differential system: susceptible, exposed, infected, and recovered. Three different cases of the model are taken and numerically presented by applying the stochastic SCGGNNs. An activation function 'log-sigmoid' uses twenty neurons in the hidden layers. The precision of SCGGNNs is obtained by comparing the proposed and database solutions. While the negligible absolute error is performed around 10-06 to 10-07, it enhances the accuracy of the scheme. The obtained results of the breathing transmission epidemic system have been provided using the training, verification, and testing procedures to reduce the mean square error. Moreover, the exactness and capability of the stochastic SCGGNNs are approved through error histograms, regression values, correlation tests, and state transitions.
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Affiliation(s)
- Najah AbuAli
- College of Information Technology, UAE University, P. O. Box 15551, Al Ain, UAE.
| | - Muhammad Bilal Khan
- College of Information Technology, UAE University, P. O. Box 15551, Al Ain, UAE
| | - Zulqurnain Sabir
- Department of Mathematical Sciences, UAE University, P. O. Box 15551, Al Ain, UAE
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
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26
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Khan IU, Mustafa S, Shokri A, Li S, Akgül A, Bariq A. The stability analysis of a nonlinear mathematical model for typhoid fever disease. Sci Rep 2023; 13:15284. [PMID: 37714901 PMCID: PMC10504385 DOI: 10.1038/s41598-023-42244-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 09/07/2023] [Indexed: 09/17/2023] Open
Abstract
Typhoid fever is a contagious disease that is generally caused by bacteria known as Salmonella typhi. This disease spreads through manure contamination of food or water and infects unprotected people. In this work, our focus is to numerically examine the dynamical behavior of a typhoid fever nonlinear mathematical model. To achieve our objective, we utilize a conditionally stable Runge-Kutta scheme of order 4 (RK-4) and an unconditionally stable non-standard finite difference (NSFD) scheme to better understand the dynamical behavior of the continuous model. The primary advantage of using the NSFD scheme to solve differential equations is its capacity to discretize the continuous model while upholding crucial dynamical properties like the solutions convergence to equilibria and its positivity for all finite step sizes. Additionally, the NSFD scheme does not only address the deficiencies of the RK-4 scheme, but also provides results that are consistent with the continuous system's solutions. Our numerical results demonstrate that RK-4 scheme is dynamically reliable only for lower step size and, consequently cannot exactly retain the important features of the original continuous model. The NSFD scheme, on the other hand, is a strong and efficient method that presents an accurate portrayal of the original model. The purpose of developing the NSFD scheme for differential equations is to make sure that it is dynamically consistent, which means to discretize the continuous model while keeping significant dynamical properties including the convergence of equilibria and positivity of solutions for all step sizes. The numerical simulation also indicates that all the dynamical characteristics of the continuous model are conserved by discrete NSFD scheme. The theoretical and numerical results in the current work can be engaged as a useful tool for tracking the occurrence of typhoid fever disease.
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Affiliation(s)
- Ihsan Ullah Khan
- Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, 29050, KPK, Pakistan
| | - Shahbaz Mustafa
- Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, 29050, KPK, Pakistan
| | - Ali Shokri
- Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, 83111-55181, Iran
| | - Shuo Li
- School of Mathematics and Data Sciences, Changji University, Changji, 831100, Xinjiang, People's Republic of China
| | - Ali Akgül
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, 5053, Lebanon
- Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, 99138, Nicosia, Mersin, Turkey
- Department of Mathematics, Art and Science Faculty, Siirt University, 56100, Siirt, Turkey
| | - Abdul Bariq
- Department of Mathematics, Laghman University, Mehtarlam City, Laghman, 2701, Afghanistan.
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27
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Chu YM, Rashid S, Karim S, Khalid A, Elagan SK. Deterministic-stochastic analysis of fractional differential equations malnutrition model with random perturbations and crossover effects. Sci Rep 2023; 13:14824. [PMID: 37684316 PMCID: PMC10491687 DOI: 10.1038/s41598-023-41861-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 09/01/2023] [Indexed: 09/10/2023] Open
Abstract
To boost the handful of nutrient-dense individuals in the societal structure, adequate health care documentation and comprehension are permitted. This will strengthen and optimize the well-being of the community, particularly the girls and women of the community that are welcoming the new generation. In this article, we extensively explored a deterministic-stochastic malnutrition model involving nonlinear perturbation via piecewise fractional operators techniques. This novel concept leads us to analyze and predict the process from the beginning to the end of the well-being growth, as it offers the possibility to observe many behaviors from cross over to stochastic processes. Moreover, the piecewise differential operators, which can be constructed with operators such as classical, Caputo, Caputo-Fabrizio, Atangana-Baleanu and stochastic derivative. The threshold parameter is developed and the role of malnutrition in society is examined. Through a rigorous analysis, we first demonstrated that the stochastic model's solution is positive and global. Then, using appropriate stochastic Lyapunov candidates, we examined whether the stochastic system acknowledges a unique ergodic stationary distribution. The objective of this investigation is to design a nutritional deficiency in pregnant women using a piecewise fractional differential equation scheme. We examined multiple options and outlined numerical methods of coping with problems. To exemplify the effectiveness of the suggested concept, graphical conclusions, including chaotic and random perturbation patterns, are supplied. Consequently, fractional calculus' innovative aspects provide more powerful and flexible layouts, enabling us to more effectively adapt to the system dynamics tendencies of real-world representations. This has opened new doors to readers in different disciplines and enabled them to capture different behaviors at different time intervals.
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Affiliation(s)
- Yu-Ming Chu
- Department of Mathematics, Faculty of Sciences, Huzhou University, Huzhou, China
| | - Saima Rashid
- Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan.
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1401, Lebanon.
| | - Shazia Karim
- Department of Basic Sciences and Humanities, UET Lahore, Faisalabad Campus, 54800, Pakistan
| | - Aasma Khalid
- Department of Mathematics, Government College for Women University, Faisalabad, Pakistan
| | - S K Elagan
- Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, 21944, Taif, Saudi Arabia
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28
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Ramaj T, Zou X. On the treatment of melanoma: A mathematical model of oncolytic virotherapy. Math Biosci 2023; 365:109073. [PMID: 37660975 DOI: 10.1016/j.mbs.2023.109073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Revised: 08/02/2023] [Accepted: 08/28/2023] [Indexed: 09/05/2023]
Abstract
We develop and analyze a mathematical model of oncolytic virotherapy in the treatment of melanoma. We begin with a special, local case of the model, in which we consider the dynamics of the tumour cells in the presence of an oncolytic virus at the primary tumour site. We then consider the more general regional model, in which we incorporate a linear network of lymph nodes through which the tumour cells and the oncolytic virus may spread. The modelling also considers the impact of hypoxia on the disease dynamics. The modelling takes into account both the effects of hypoxia on tumour growth and spreading, as well as the impact of hypoxia on oncolytic virotherapy as a treatment modality. We find that oxygen-rich environments are favourable for the use of adenoviruses as oncolytic agents, potentially suggesting the use of complementary external oxygenation as a key aspect of treatment. Furthermore, the delicate balance between a virus' infection capabilities and its oncolytic capabilities should be considered when engineering an oncolytic virus. If the virus is too potent at killing tumour cells while not being sufficiently effective at infecting them, the infected tumour cells are destroyed faster than they are able to infect additional tumour cells, leading less favourable clinical results. Numerical simulations are performed in order to support the analytic results and to further investigate the impact of various parameters on the outcomes of treatment. Our modelling provides further evidence indicating the importance of three key factors in treatment outcomes: tumour microenvironment oxygen concentration, viral infection rates, and viral oncolysis rates. The numerical results also provide some estimates on these key model parameters which may be useful in the engineering of oncolytic adenoviruses.
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Affiliation(s)
- Tedi Ramaj
- Department of Mathematics, Western University, London, On Canada.
| | - Xingfu Zou
- Department of Mathematics, Western University, London, On Canada
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29
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Ziarelli G, Dede' L, Parolini N, Verani M, Quarteroni A. Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: An application to the Italian scenario. Infect Dis Model 2023; 8:672-703. [PMID: 37346476 PMCID: PMC10240908 DOI: 10.1016/j.idm.2023.05.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Revised: 05/15/2023] [Accepted: 05/29/2023] [Indexed: 06/23/2023] Open
Abstract
In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.
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Affiliation(s)
| | - Luca Dede'
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - Nicola Parolini
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - Marco Verani
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - Alfio Quarteroni
- MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
- Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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30
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You W, Ren J, Zhang Q. Finite-time contraction stability of a stochastic reaction-diffusion dengue model with impulse and Markov switching. Math Biosci Eng 2023; 20:16978-17002. [PMID: 37920043 DOI: 10.3934/mbe.2023757] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/04/2023]
Abstract
From the perspective of prevention and treatment of dengue, it is important to minimize the number of infections within a limited time frame. That is, the study of finite time contraction stability (FTCS) of dengue system is a meaningful topic. This article proposes a dengue epidemic model with reaction-diffusion, impulse and Markov switching. By constructing an equivalent system, the well-posedness of the positive solution is proved. The main result is that sufficient conditions to guarantee the finite time contraction stability of the dengue model are acquired based on the average pulse interval method and the bounded pulse interval method. Furthermore, the numerical findings indicate the influences of impulse, control strategies and noise intensity on the FTCS.
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Affiliation(s)
- Wei You
- School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
| | - Jie Ren
- School of Medical Information and Engineering, Ningxia Medical University, Yinchuan 750004, China
| | - Qimin Zhang
- School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
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31
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Kabir KMA, Islam MDS, Sharif Ullah M. Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology. Vaccines (Basel) 2023; 11:1421. [PMID: 37766098 PMCID: PMC10536494 DOI: 10.3390/vaccines11091421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2023] [Revised: 07/19/2023] [Accepted: 07/20/2023] [Indexed: 09/29/2023] Open
Abstract
Explaining how individual choice and government policy can appear in the same context in real society is one of the most challenging scientific problems. Controlling infectious diseases requires effective prevention and control measures, including vaccination and self-defense measures. In this context, optimal control strategies incorporating vaccination and self-defense measures have been proposed using the framework of evolutionary game theory. This approach accounts for individuals' behavior and interactions in a population. It can provide insights into the effectiveness of different strategies for controlling the spread of infectious diseases. The optimal control strategy involves balancing the costs and benefits of vaccination, considering the dynamic interplay between the infected and susceptible populations. By combining evolutionary game theory with optimal control theory, we can identify the optimal allocation of resources for vaccination and self-defense measures, which can maximize the control of infectious diseases while minimizing costs. The model is utilized to analyze public health policies diseases, such as vaccination and self-defense strategies, to mitigate the spread of infectious in the context of delayed decision-making.
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Affiliation(s)
- K. M. Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
| | - MD Shahidul Islam
- Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka 1207, Bangladesh;
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32
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Avusuglo WS, Bragazzi N, Asgary A, Orbinski J, Wu J, Kong JD. Leveraging an epidemic-economic mathematical model to assess human responses to COVID-19 policies and disease progression. Sci Rep 2023; 13:12842. [PMID: 37553397 PMCID: PMC10409770 DOI: 10.1038/s41598-023-39723-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 07/29/2023] [Indexed: 08/10/2023] Open
Abstract
It is imperative that resources are channelled towards programs that are efficient and cost effective in combating the spread of COVID-19, the disease caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). This study proposed and analyzed control strategies for that purpose. We developed a mathematical disease model within an optimal control framework that allows us to investigate the best approach for curbing COVID-19 epidemic. We address the following research question: what is the role of community compliance as a measure for COVID-19 control? Analyzing the impact of community compliance of recommended guidelines by health authorities-examples, social distancing, face mask use, and sanitizing-coupled with efforts by health authorities in areas of vaccine provision and effective quarantine-showed that the best intervention in addition to implementing vaccination programs and effective quarantine measures, is the active incorporation of individuals' collective behaviours, and that resources should also be directed towards community campaigns on the importance of face mask use, social distancing, and frequent sanitizing, and any other collective activities. We also demonstrated that collective behavioral response of individuals influences the disease dynamics; implying that recommended health policy should be contextualized.
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Affiliation(s)
- Wisdom S Avusuglo
- Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), Laboratory for Industrial and Applied Mathematics, York University, Toronto, Canada
| | - Nicola Bragazzi
- Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), Laboratory for Industrial and Applied Mathematics, York University, Toronto, Canada
| | - Ali Asgary
- Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), The Advanced Disaster, Emergency and Rapid Response Program, York University, Toronto, Canada
| | - James Orbinski
- Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), The Dahdaleh Institute for Global Health Research, York University, Toronto, Canada
| | - Jianhong Wu
- Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), Laboratory for Industrial and Applied Mathematics, York University, Toronto, Canada
| | - Jude Dzevela Kong
- Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), Laboratory for Industrial and Applied Mathematics, York University, Toronto, Canada.
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33
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Wei Q, Wang W, Zhou H, Metzler R, Chechkin A. Time-fractional Caputo derivative versus other integrodifferential operators in generalized Fokker-Planck and generalized Langevin equations. Phys Rev E 2023; 108:024125. [PMID: 37723675 DOI: 10.1103/physreve.108.024125] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2023] [Accepted: 07/21/2023] [Indexed: 09/20/2023]
Abstract
Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous diffusion in a large variety of complex systems. The equivalent formulations in terms of Caputo or Riemann-Liouville fractional derivatives can be derived as continuum limits of continuous-time random walks and are associated with the Mittag-Leffler relaxation of Fourier modes, interpolating between a short-time stretched exponential and a long-time inverse power-law scaling. More recently, a number of other integrodifferential operators have been proposed, including the Caputo-Fabrizio and Atangana-Baleanu forms. Moreover, the conformable derivative has been introduced. We study here the dynamics of the associated generalized Fokker-Planck equations from the perspective of the moments, the time-averaged mean-squared displacements, and the autocovariance functions. We also study generalized Langevin equations based on these generalized operators. The differences between the Fokker-Planck and Langevin equations with different integrodifferential operators are discussed and compared with the dynamic behavior of established models of scaled Brownian motion and fractional Brownian motion. We demonstrate that the integrodifferential operators with exponential and Mittag-Leffler kernels are not suitable to be introduced to Fokker-Planck and Langevin equations for the physically relevant diffusion scenarios discussed in our paper. The conformable and Caputo Langevin equations are unveiled to share similar properties with scaled and fractional Brownian motion, respectively.
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Affiliation(s)
- Qing Wei
- School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, People's Republic of China
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
| | - Wei Wang
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
| | - Hongwei Zhou
- School of Energy and Mining Engineering, China University of Mining and Technology, Beijing 100083, People's Republic of China
| | - Ralf Metzler
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Aleksei Chechkin
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
- Akhiezer Institute for Theoretical Physics National Science Center, Kharkiv Institute of Physics and Technology, Akademichna 1, Kharkiv 61108, Ukraine
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34
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Su X, Sun Y, Liu H, Lang Q, Zhang Y, Zhang J, Wang C, Chen Y. An innovative ensemble model based on deep learning for predicting COVID-19 infection. Sci Rep 2023; 13:12322. [PMID: 37516796 PMCID: PMC10387055 DOI: 10.1038/s41598-023-39408-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Accepted: 07/25/2023] [Indexed: 07/31/2023] Open
Abstract
Nowadays, global public health crises are occurring more frequently, and accurate prediction of these diseases can reduce the burden on the healthcare system. Taking COVID-19 as an example, accurate prediction of infection can assist experts in effectively allocating medical resources and diagnosing diseases. Currently, scholars worldwide use single model approaches or epidemiology models more often to predict the outbreak trend of COVID-19, resulting in poor prediction accuracy. Although a few studies have employed ensemble models, there is still room for improvement in their performance. In addition, there are only a few models that use the laboratory results of patients to predict COVID-19 infection. To address these issues, research efforts should focus on improving disease prediction performance and expanding the use of medical disease prediction models. In this paper, we propose an innovative deep learning model Whale Optimization Convolutional Neural Networks (CNN), Long-Short Term Memory (LSTM) and Artificial Neural Network (ANN) called WOCLSA which incorporates three models ANN, CNN and LSTM. The WOCLSA model utilizes the Whale Optimization Algorithm to optimize the neuron number, dropout and batch size parameters in the integrated model of ANN, CNN and LSTM, thereby finding the global optimal solution parameters. WOCLSA employs 18 patient indicators as predictors, and compares its results with three other ensemble deep learning models. All models were validated with train-test split approaches. We evaluate and compare our proposed model and other models using accuracy, F1 score, recall, AUC and precision metrics. Through many studies and tests, our results show that our prediction models can identify patients with COVID-19 infection at the AUC of 91%, 91%, and 93% respectively. Other prediction results achieve a respectable accuracy of 92.82%, 92.79%, and 91.66% respectively, f1-score of 93.41%, 92.79%, and 92.33% respectively, precision of 93.41%, 92.79%, and 92.33% respectively, recall of 93.41%, 92.79%, and 92.33% respectively. All of these exceed 91%, surpassing those of comparable models. The execution time of WOCLSA is also an advantage. Therefore, the WOCLSA ensemble model can be used to assist in verifying laboratory research results and predict and to judge various diseases in public health events.
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Affiliation(s)
- Xiaoying Su
- School of Jilin Emergency Management, Changchun Institute of Technology, Changchun, 130021, China
| | - Yanfeng Sun
- College of Computer Science and Technology, Jilin University, Changchun, 130012, China
| | - Hongxi Liu
- School of Jilin Emergency Management, Changchun Institute of Technology, Changchun, 130021, China
| | - Qiuling Lang
- School of Jilin Emergency Management, Changchun Institute of Technology, Changchun, 130021, China
| | - Yichen Zhang
- School of Jilin Emergency Management, Changchun Institute of Technology, Changchun, 130021, China
| | - Jiquan Zhang
- School of Environment, Northeast Normal University, Changchun, 130024, China
| | - Chaoyong Wang
- School of Jilin Emergency Management, Changchun Institute of Technology, Changchun, 130021, China.
| | - Yanan Chen
- School of Jilin Emergency Management, Changchun Institute of Technology, Changchun, 130021, China
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35
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Aljohani HM, Ahsan-Ul-Haq M, Zafar J, Almetwally EM, Alghamdi AS, Hussam E, Muse AH. Analysis of Covid-19 data using discrete Marshall-Olkinin Length Biased Exponential: Bayesian and frequentist approach. Sci Rep 2023; 13:12243. [PMID: 37507438 PMCID: PMC10382491 DOI: 10.1038/s41598-023-39183-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2023] [Accepted: 07/20/2023] [Indexed: 07/30/2023] Open
Abstract
The paper presents a novel statistical approach for analyzing the daily coronavirus case and fatality statistics. The survival discretization method was used to generate a two-parameter discrete distribution. The resulting distribution is referred to as the "Discrete Marshall-Olkin Length Biased Exponential (DMOLBE) distribution". Because of the varied forms of its probability mass and failure rate functions, the DMOLBE distribution is adaptable. We calculated the mean and variance, skewness, kurtosis, dispersion index, hazard and survival functions, and second failure rate function for the suggested distribution. The DI index demonstrates that the proposed model can represent both over-dispersed and under-dispersed data sets. We estimated the parameters of the DMOLBE distribution. The behavior of ML estimates is checked via a comprehensive simulation study. The behavior of Bayesian estimates is checked by generating 10,000 iterations of Markov chain Monte Carlo techniques, plotting the trace, and checking the proposed distribution. From simulation studies, it was observed that the bias and mean square error decreased with an increase in sample size. To show the importance and flexibility of DMOLBE distribution using two data sets about deaths due to coronavirus in China and Pakistan are analyzed. The DMOLBE distribution provides a better fit than some important discrete models namely the discrete Burr-XII, discrete Bilal, discrete Burr-Hatke, discrete Rayleigh distribution, and Poisson distributions. We conclude that the new proposed distribution works well in analyzing these data sets. The data sets used in the paper was collected from 2020 year.
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Affiliation(s)
- Hassan M Aljohani
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia
| | - Muhammad Ahsan-Ul-Haq
- College of Statistical and Actuarial Sciences, University of the Punjab, Lahore, Pakistan
| | - Javeria Zafar
- College of Statistical and Actuarial Sciences, University of the Punjab, Lahore, Pakistan
| | - Ehab M Almetwally
- Faculty of Business Administration, Delta University of Science and Technology, Gamasa, 11152, Egypt
- Scientific Association for Applied Studies and Research (SAASR), Al Manzalah, Egypt
| | - Abdulaziz S Alghamdi
- College of Science and Arts, King Abdulaziz University, P. O. Box 344, 21911, Rabigh, Saudi Arabia
| | - Eslam Hussam
- Department of Mathematics, Faculty of Science, Helwan University, Helwan, Egypt
| | - Abdisalam Hassan Muse
- Faculty of Science and Humanities, School of Postgraduate Studies and Research (SPGSR), Amoud University, Borama, 25263, Somalia.
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36
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Hyder AA. New Fractional Inequalities through Convex Functions and Comprehensive Riemann–Liouville Integrals. Journal of Mathematics 2023; 2023:1-10. [DOI: 10.1155/2023/9532488] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
In most fields of applied sciences, inequalities are important in constructing mathematical systems and associated solution functions. Convexity also has a significant impact on an assortment of mathematical topics. By utilizing a comprehensive version of Riemann–Liouville integrals and the functions’ convexity condition, we present and prove novel fractional inequalities. According to the current literature, this work is a novel addition to the literature, and the proposed technique for addressing fractional inequalities issues is straightforward and simple to execute. It is also easy to see that all of the inequalities that have been developed are inclusive and may be reduced to a variety of other inequalities that have been proposed in the literature. Additionally, certain numeric examples with graphs are provided to support the theoretical results.
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Affiliation(s)
- Abd-Allah Hyder
- Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
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37
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Přibylová L, Eclerová V, Májek O, Jarkovský J, Pavlík T, Dušek L. Using real-time ascertainment rate estimate from infection and hospitalization dataset for modeling the spread of infectious disease: COVID-19 case study in the Czech Republic. PLoS One 2023; 18:e0287959. [PMID: 37440522 PMCID: PMC10343065 DOI: 10.1371/journal.pone.0287959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2021] [Accepted: 06/09/2023] [Indexed: 07/15/2023] Open
Abstract
We present a novel approach to estimate the time-varying ascertainment rate in almost real-time, based on the surveillance of positively tested infectious and hospital admission data. We also address the age dependence of the estimate. The ascertainment rate estimation is based on the Bayes theorem. It can be easily calculated and used (i) as part of a mechanistic model of the disease spread or (ii) to estimate the unreported infections or changes in their proportion in almost real-time as one of the early-warning signals in case of undetected outbreak emergence. The paper also contains a case study of the COVID-19 epidemic in the Czech Republic. The case study demonstrates the usage of the ascertainment rate estimate in retrospective analysis, epidemic monitoring, explanations of differences between waves, usage in the national Anti-epidemic system, and monitoring of the effectiveness of non-pharmaceutical interventions on Czech nationwide surveillance datasets. The Czech data reveal that the probability of hospitalization due to SARS-CoV-2 infection for the senior population was 12 times higher than for the non-senior population in the monitored period from the beginning of March 2020 to the end of May 2021. In a mechanistic model of COVID-19 spread in the Czech Republic, the ascertainment rate enables us to explain the links between all basic compartments, including new cases, hospitalizations, and deaths.
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Affiliation(s)
- Lenka Přibylová
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Veronika Eclerová
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
- RECETOX, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Ondřej Májek
- Institute of Biostatistics and Analyses, Faculty of Medicine, Masaryk University, Brno, Czech Republic
- Institute of Health Information and Statistics of the Czech Republic
| | - Jiří Jarkovský
- Institute of Biostatistics and Analyses, Faculty of Medicine, Masaryk University, Brno, Czech Republic
- Institute of Health Information and Statistics of the Czech Republic
| | - Tomáš Pavlík
- Institute of Biostatistics and Analyses, Faculty of Medicine, Masaryk University, Brno, Czech Republic
- Institute of Health Information and Statistics of the Czech Republic
| | - Ladislav Dušek
- Institute of Biostatistics and Analyses, Faculty of Medicine, Masaryk University, Brno, Czech Republic
- Institute of Health Information and Statistics of the Czech Republic
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38
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Malinzi J, Juma VO, Madubueze CE, Mwaonanji J, Nkem GN, Mwakilama E, Mupedza TV, Chiteri VN, Bakare EA, Moyo ILZ, Campillo-Funollet E, Nyabadza F, Madzvamuse A. COVID-19 transmission dynamics and the impact of vaccination: modelling, analysis and simulations. R Soc Open Sci 2023; 10:221656. [PMID: 37501660 PMCID: PMC10369038 DOI: 10.1098/rsos.221656] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 07/03/2023] [Indexed: 07/29/2023]
Abstract
Despite the lifting of COVID-19 restrictions, the COVID-19 pandemic and its effects remain a global challenge including the sub-Saharan Africa (SSA) region. Knowledge of the COVID-19 dynamics and its potential trends amidst variations in COVID-19 vaccine coverage is therefore crucial for policy makers in the SSA region where vaccine uptake is generally lower than in high-income countries. Using a compartmental epidemiological model, this study aims to forecast the potential COVID-19 trends and determine how long a wave could be, taking into consideration the current vaccination rates. The model is calibrated using South African reported data for the first four waves of COVID-19, and the data for the fifth wave are used to test the validity of the model forecast. The model is qualitatively analysed by determining equilibria and their stability, calculating the basic reproduction number R0 and investigating the local and global sensitivity analysis with respect to R0. The impact of vaccination and control interventions are investigated via a series of numerical simulations. Based on the fitted data and simulations, we observed that massive vaccination would only be beneficial (deaths averting) if a highly effective vaccine is used, particularly in combination with non-pharmaceutical interventions. Furthermore, our forecasts demonstrate that increased vaccination coverage in SSA increases population immunity leading to low daily infection numbers in potential future waves. Our findings could be helpful in guiding policy makers and governments in designing vaccination strategies and the implementation of other COVID-19 mitigation strategies.
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Affiliation(s)
- Joseph Malinzi
- Faculty of Science and Engineering, Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Swaziland
- Institute of Systems Science, Durban University of Technology, Durban 4000, South Africa
| | - Victor Ogesa Juma
- Multiscale in Mechanical and Biological Engineering (M2BE), Instituto de Investigación en Ingeniería de Aragón (I3A), University of Zaragoza, 50018 Zaragoza, Spain
| | - Chinwendu Emilian Madubueze
- Department of Mathematics, Federal University of Agriculture, Makurdi, Nigeria
- Department of Mathematics and Statistics, York University, Toronto, Canada
| | - John Mwaonanji
- Department of Mathematical Sciences, Malawi University of Business and Applied Sciences, Blantyre, Malawi
| | | | - Elias Mwakilama
- Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
| | - Tinashe Victor Mupedza
- Department of Mathematics & Computational Sciences, University of Zimbabwe, Box MP167 Mount Pleasant, Harare, Zimbabwe
| | | | - Emmanuel Afolabi Bakare
- International Centre for Applied Mathematical Modelling and Data Analytics, Federal University Oye-Ekiti, Ekiti State, Nigeria
- Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria
| | - Isabel Linda-Zulu Moyo
- Faculty of Science and Engineering, Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Swaziland
| | | | - Farai Nyabadza
- Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park 2006, South Africa
| | - Anotida Madzvamuse
- Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park 2006, South Africa
- Mathematics Department, Room 121, Mathematics Building, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2
- School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
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de Vasconcelos ASV, de Lima JS, Cardoso RTN. Multiobjective optimization to assess dengue control costs using a climate-dependent epidemiological model. Sci Rep 2023; 13:10271. [PMID: 37355697 PMCID: PMC10290689 DOI: 10.1038/s41598-023-36903-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2023] [Accepted: 06/12/2023] [Indexed: 06/26/2023] Open
Abstract
Arboviruses, diseases transmitted by arthropods, have become a significant challenge for public health managers. The World Health Organization highlights dengue as responsible for millions of infections worldwide annually. As there is no specific treatment for the disease and no free-of-charge vaccine for mass use in Brazil, the best option is the measures to combat the vector, the Aedes aegypti mosquito. Therefore, we proposed an epidemiological model dependent on temperature, precipitation, and humidity, considering symptomatic and asymptomatic dengue infections. Through computer simulations, we aimed to minimize the amount of insecticides and the social cost demanded to treat patients. We proposed a case study in which our model is fitted with real data from symptomatic dengue-infected humans in an epidemic year in a Brazilian city. Our multiobjective optimization model considers an additional control using larvicide, adulticide, and ultra-low volume spraying. The work's main contribution is studying the monetary cost of the actions to combat the vector demand versus the hospital cost per confirmed infected, comparing approaches with and without additional control. Results showed that the additional vector control measures are cheaper than the hospital treatment without the vector control would be.
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Affiliation(s)
- Amália Soares Vieira de Vasconcelos
- Postgraduate Program in Mathematical and Computational Modeling (PPGMMC), Federal Center for Technological Education-CEFET-MG, Av. Amazonas, 7675, Nova Gameleira, Belo Horizonte, Minas Gerais, 30510-000, Brazil.
| | - Josenildo Silva de Lima
- Postgraduate Program in Mathematical and Computational Modeling (PPGMMC), Federal Center for Technological Education-CEFET-MG, Av. Amazonas, 7675, Nova Gameleira, Belo Horizonte, Minas Gerais, 30510-000, Brazil
| | - Rodrigo Tomás Nogueira Cardoso
- Department of Mathematics, Federal Center for Technological Education-CEFET-MG, Av. Amazonas, 7675, Nova Gameleira, Belo Horizonte, Minas Gerais, 30510-000, Brazil
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Xue L, Jin X, Zhu H. Assessing the impact of serostatus-dependent immunization on mitigating the spread of dengue virus. J Math Biol 2023; 87:5. [PMID: 37301798 DOI: 10.1007/s00285-023-01944-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Revised: 05/29/2023] [Accepted: 05/29/2023] [Indexed: 06/12/2023]
Abstract
Dengue is the most rapidly spreading mosquito-borne disease that poses great threats to public health. We propose a compartmental model with primary and secondary infection and targeted vaccination to assess the impact of serostatus-dependent immunization on mitigating the spread of dengue virus. We derive the basic reproduction number and investigate the stability and bifurcations of the disease-free equilibrium and endemic equilibria. The existence of a backward bifurcation is proved and is used to explain the threshold dynamics of the transmission. We also carry out numerical simulations and present bifurcation diagrams to reveal rich dynamics of the model such as bi-stability of the equilibria, limit cycles, and chaos. We prove the uniform persistence and global stability of the model. Sensitivity analysis suggests that mosquito control and protection from mosquito bites are still the key measures of controlling the spread of dengue virus, though serostatus-dependent immunization is implemented. Our findings provide insightful information for public health in mitigating dengue epidemics through vaccination.
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Affiliation(s)
- Ling Xue
- College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, Heilongjiang, China.
| | - Xiulei Jin
- College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, Heilongjiang, China
| | - Huaiping Zhu
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, Centre for Diseases Modelling (CDM), York University, Toronto, Canada.
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Wacker B, Schlüter JC. A non-standard finite-difference-method for a non-autonomous epidemiological model: analysis, parameter identification and applications. Math Biosci Eng 2023; 20:12923-12954. [PMID: 37501473 DOI: 10.3934/mbe.2023577] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
In this work, we propose a new non-standard finite-difference-method for the numerical solution of the time-continuous non-autonomous susceptible-infected-recovered model. For our time-discrete numerical solution algorithm, we prove preservation of non-negativity and show that the unique time-discrete solution converges linearly towards the time-continuous unique solution. In addition to that, we introduce a parameter identification algorithm for the susceptible-infected-recovered model. Finally, we provide two numerical examples to stress our theoretical findings.
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Affiliation(s)
- Benjamin Wacker
- Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg, Eberhard-Leibnitz-Str. 2, D-06217 Merseburg, Germany
- Chair of Data Science, Faculty of Management, Social Work and Construction, HAWK, Haarmannplatz 3, D-37603 Holzminden, Germany
| | - Jan Christian Schlüter
- Chair of Data Science, Faculty of Management, Social Work and Construction, HAWK, Haarmannplatz 3, D-37603 Holzminden, Germany
- Computational Epidemiology and Public Health Research Group, Institute for Medical Epidemiology, Biometrics and Informatics, Interdisciplinary Center for Health Sciences, Martin Luther University Halle-Wittenberg, Magdeburger Str. 8, D-06112 Halle, Germany
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Kifle ZS, Obsu LL. Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application. Infect Dis Model 2023; 8:574-602. [PMID: 37287990 PMCID: PMC10229442 DOI: 10.1016/j.idm.2023.05.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Revised: 05/06/2023] [Accepted: 05/26/2023] [Indexed: 06/09/2023] Open
Abstract
COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R0 < 1 and the exogenous reinfection rate greater than a threshold (η > η∗). The analytical results show that reducing R0 < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.
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Affiliation(s)
| | - Legesse Lemecha Obsu
- Department of Mathematics, Adama Science and Technology University, Adama, Ethiopia
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Edelman M, Helman AB, Smidtaite R. Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < α < 1. Chaos 2023; 33:2894482. [PMID: 37276566 DOI: 10.1063/5.0151812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 05/04/2023] [Indexed: 06/07/2023]
Abstract
In this paper, we investigate the generalized fractional maps of the orders 0<α<1. Commonly used in publications, fractional and fractional difference maps of the orders 0<α<1 belong to this class of maps. As an example, we numerically solve the equations, which define asymptotically periodic points to draw the bifurcation diagrams for the fractional difference logistic map with α=0.5. For periods more than four (T>4), these bifurcation diagrams are significantly different from the bifurcation diagrams obtained after 105 iterations on individual trajectories. We present examples of transition to chaos on individual trajectories with positive and zero Lyapunov exponents. We derive the algebraic equations, which allow the calculation of bifurcation points of generalized fractional maps. We use these equations to calculate the bifurcation points for the fractional and fractional difference logistic maps with α=0.5. The results of our numerical simulations allow us to make a conjecture that the cascade of bifurcations scenarios of transition to chaos in generalized fractional maps and regular maps are similar, and the value of the generalized fractional Feigenbaum constant δf is the same as the value of the regular Feigenbaum constant δ=4.669….
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Affiliation(s)
- Mark Edelman
- Stern College for Women, Yeshiva University, 245 Lexington Ave., New York, New York 10016, USA
- Courant Institute of Mathematical Sciences at NYU, 251 Mercer Street, New York, New York 10012, USA
| | - Avigayil B Helman
- Department of Computer Science, Columbia University, 500 W. 120th Street, New York, New York 10027, USA
| | - Rasa Smidtaite
- Department of Applied Mathematics, Kaunas University of Technology, Studentu 50-429, 51368 Kaunas, Lithuania
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Chu YM, Rashid S, Akdemir AO, Khalid A, Baleanu D, Al-Sinan BR, Elzibar OAI. Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model. Results Phys 2023; 49:106467. [PMID: 37153140 PMCID: PMC10140436 DOI: 10.1016/j.rinp.2023.106467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Revised: 04/13/2023] [Accepted: 04/17/2023] [Indexed: 05/09/2023]
Abstract
The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R 0 . Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelöf technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R 0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.
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Affiliation(s)
- Yu-Ming Chu
- Department of Mathematics, Huzhou University, Huzhou, 313000, China
| | - Saima Rashid
- Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
| | - Ahmet Ocak Akdemir
- Department of Mathematics, Faculty of Science and Arts, Agri Ibrahim Cecen University, Agrı, Turkey
| | - Aasma Khalid
- Department of Mathematics, Government College women University, Faisalabad, Pakistan
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, 06530 Bucharest, Romania
- Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, Lebanon
| | - Bushra R Al-Sinan
- University of Hafr Al-Batin, Nairiyah College, Department of Administrative and Financial Sciences, Saudi Arabia
| | - O A I Elzibar
- Department of Mathematics, Turabah University College, Taif University, P.O. Box 1109, Taif 21944, Saudi Arabia
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Roul P, Rohil V, Espinosa-Paredes G, Obaidurrahman K. An efficient computational technique for solving a fractional-order model describing dynamics of neutron flux in a nuclear reactor. ANN NUCL ENERGY 2023. [DOI: 10.1016/j.anucene.2023.109733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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Khalaf SL, Kadhim MS, Khudair AR. Studying of COVID-19 fractional model: Stability analysis. Partial Differ Equ Appl Math 2023; 7:100470. [PMID: 36505269 PMCID: PMC9721170 DOI: 10.1016/j.padiff.2022.100470] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Revised: 11/23/2022] [Accepted: 12/02/2022] [Indexed: 12/12/2022]
Abstract
This article focuses on the recent epidemic caused by COVID-19 and takes into account several measures that have been taken by governments, including complete closure, media coverage, and attention to public hygiene. It is well known that mathematical models in epidemiology have helped determine the best strategies for disease control. This motivates us to construct a fractional mathematical model that includes quarantine categories as well as government sanctions. In this article, we prove the existence and uniqueness of positive bounded solutions for the suggested model. Also, we investigate the stability of the disease-free and endemic equilibriums by using the basic reproduction number (BRN). Moreover, we investigate the stability of the considering model in the sense of Ulam-Hyers criteria. To underpin and demonstrate this study, we provide a numerical simulation, whose results are consistent with the analysis presented in this article.
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Herrera-Serrano JE, Guerrero-Díaz-de-León JA, Medina-Ramírez IE, Macías-Díaz JE. A multiconsistent computational methodology to resolve a diffusive epidemiological system with effects of migration, vaccination and quarantine. Comput Methods Programs Biomed 2023; 236:107526. [PMID: 37098304 DOI: 10.1016/j.cmpb.2023.107526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 03/21/2023] [Accepted: 04/02/2023] [Indexed: 05/21/2023]
Abstract
BACKGROUND We provide a compartmental model for the transmission of some contagious illnesses in a population. The model is based on partial differential equations, and takes into account seven sub-populations which are, concretely, susceptible, exposed, infected (asymptomatic or symptomatic), quarantined, recovered and vaccinated individuals along with migration. The goal is to propose and analyze an efficient computer method which resembles the dynamical properties of the epidemiological model. MATERIALS AND METHODS A non-local approach is utilized for finding approximate solutions for the mathematical model. To that end, a non-standard finite-difference technique is introduced. The finite-difference scheme is a linearly implicit model which may be rewritten using a suitable matrix. Under suitable circumstances, the matrices representing the methodology are M-matrices. RESULTS Analytically, the local asymptotic stability of the constant solutions is investigated and the next generation matrix technique is employed to calculate the reproduction number. Computationally, the dynamical consistency of the method and the numerical efficiency are investigated rigorously. The method is thoroughly examined for its convergence, stability, and consistency. CONCLUSIONS The theoretical analysis of the method shows that it is able to maintain the positivity of its solutions and identify equilibria. The method's local asymptotic stability properties are similar to those of the continuous system. The analysis concludes that the numerical model is convergent, stable and consistent, with linear order of convergence in the temporal domain and quadratic order of convergence in the spatial variables. A computer implementation is used to confirm the mathematical properties, and it confirms the ability in our scheme to preserve positivity, and identify equilibrium solutions and their local asymptotic stability.
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Affiliation(s)
- Jorge E Herrera-Serrano
- Basic Sciences Faculty, Aguascalientes Autonomous University, Ave. Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 201000, Mexico; Academic Direction of Information Technologies and Mechatronics, Technological University of the North of Aguascalientes, Ave. Universidad 1001, La Estación Rincón, Rincón de Romos, Ags. 20400, Mexico.
| | - José A Guerrero-Díaz-de-León
- Department of Statistics, Aguascalientes Autonomous University, Ave. Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20100, Mexico.
| | - Iliana E Medina-Ramírez
- Department of Chemistry, Aguascalientes Autonomous University, Ave. Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20100, Mexico.
| | - Jorge E Macías-Díaz
- Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia; Department of Mathematics and Physics, Aguascalientes Autonomous University, Ave. Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20100, Mexico.
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Zhang Y, Tai S, Zhang D, Wu L. How to promote the diffusion of green behavior among contractors? Analysis and simulation using the SIR model. J Environ Manage 2023; 335:117555. [PMID: 36842357 DOI: 10.1016/j.jenvman.2023.117555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Revised: 02/06/2023] [Accepted: 02/19/2023] [Indexed: 06/18/2023]
Abstract
To promote the green development of the construction industry, improve resource utilization, and mitigate the environmental pollution caused by engineering projects, this study identifies the key paths and influencing factors of behavioral diffusion through the analysis of green behavior diffusion among contractors based on the behavioral decisions of the main participants. The study aims to improve positive influences among contractors with respect to the sustainable development of construction. Using the SIR (susceptible-infected-removed) model, we reconsider contractors of different states; construct state transformation paths for potential adopters, adopters, and abandoners of green behaviors among contractors; and analyze the factors that influence the diffusion of green behaviors among contractors to simulate the effects of different paths of behavior diffusion. The results show that two paths, adoption and recovery rates, have a positive influence on the diffusion of green behavior, while three other paths have a negative influence. The identified factors exhibit two types of influence, promotion and hindrance, involving both intra-firm and government regulations, and are associated with other stakeholders. This study promotes the diffusion of green behavior among contractors, which allows contractors to gain a competitive advantage in advance and has positive implications for the implementation of environmentally friendly concepts in the construction industry.
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Affiliation(s)
- Yao Zhang
- School of Management Science and Real Estate, Chongqing University, Chongqing, China.
| | - Shuangliang Tai
- School of Civil Engineering, Harbin Institute of Technology, Harbin, China.
| | - Dan Zhang
- School of Public Policy and Administration, Xi'an Jiaotong University, Xi'an, China.
| | - Lei Wu
- WISDRI Engineering & Research Incorporation Limited, Wuhan, China.
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Shamsi Gamchi N, Esmaeili M. A novel mathematical model for prioritization of individuals to receive vaccine considering governmental health protocols. Eur J Health Econ 2023; 24:633-646. [PMID: 35900675 PMCID: PMC9330986 DOI: 10.1007/s10198-022-01491-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/25/2021] [Accepted: 06/09/2022] [Indexed: 05/12/2023]
Abstract
Infectious diseases drive countries to provide vaccines to individuals. Due to the limited supply of vaccines, individuals prioritize receiving vaccinations worldwide. Although, priority groups are formed based on age groupings due to the restricted decision-making time. Governments usually ordain different health protocols such as lockdown policy, mandatory use of face masks, and vaccination during the pandemics. Therefore, this study considers the case of COVID-19 with a SEQIR (susceptible-exposed-quarantined-infected-recovered) epidemic model and presents a novel prioritization technique to minimize the social and economic impacts of the lockdown policy. We use retail units as one of the affected parts to demonstrate how a vaccination plan may be more effective if individuals such as retailers were prioritized and age groups. In addition, we estimate the total required vaccine doses to control the epidemic disease and compute the number of vaccine doses supplied by various suppliers. The vaccine doses are determined using optimal control theory in the solution technique. In addition, we consider the effect of the mask using policy in the number of vaccine doses allocated to each priority group. The model's performance is evaluated using an illustrative scenario based on a real case.
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Affiliation(s)
- N Shamsi Gamchi
- Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran
| | - M Esmaeili
- Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran.
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Zaman UHM, Arefin MA, Akbar MA, Uddin MH. Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique. PLoS One 2023; 18:e0285178. [PMID: 37216390 DOI: 10.1371/journal.pone.0285178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 04/16/2023] [Indexed: 05/24/2023] Open
Abstract
Nonlinear fractional partial differential equations are highly applicable for representing a wide variety of features in engineering and research, such as shallow-water, oceanography, fluid dynamics, acoustics, plasma physics, optical fiber system, turbulence, nonlinear biological systems, and control theory. In this research, we chose to construct some new closed form solutions of traveling wave of fractional order nonlinear coupled type Boussinesq-Burger (BB) and coupled type Boussinesq equations. In beachside ocean and coastal engineering, the suggested equations are frequently used to explain the spread of shallow-water waves, depict the propagation of waves through dissipative and nonlinear media, and appears during the investigation of the flow of fluid within a dynamic system. The subsidiary extended tanh-function technique for the suggested equations is solved for achieve new results by conformable derivatives. The fractional order differential transform was used to simplify the solution process by converting fractional differential equations to ordinary type differential equations by using the mentioned method. Using this technique, some applicable wave forms of solitons like bell type, kink type, singular kink, multiple kink, periodic wave, and many other types solution were accomplished, and we express our achieve solutions by 3D, contour, list point, and vector plots by using mathematical software such as MATHEMATICA to express the physical sketch much more clearly. Moreover, we assured that the suggested technique is more reliable, pragmatic, and dependable, that also explore more general exact solutions of close form traveling waves.
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Affiliation(s)
- U H M Zaman
- Department of Mathematics, Jashore University of Science and Technology, Jashore, Bangladesh
| | - Mohammad Asif Arefin
- Department of Mathematics, Jashore University of Science and Technology, Jashore, Bangladesh
| | - M Ali Akbar
- Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
| | - M Hafiz Uddin
- Department of Mathematics, Jashore University of Science and Technology, Jashore, Bangladesh
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