1
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Korsah MA, Johnston ST, Tiedje KE, Day KP, Flegg JA, Walker CR. Mathematical Assessment of the Role of Intervention Programs for Malaria Control. Bull Math Biol 2024; 86:91. [PMID: 38888640 PMCID: PMC11189351 DOI: 10.1007/s11538-024-01321-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2023] [Accepted: 06/03/2024] [Indexed: 06/20/2024]
Abstract
Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.
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Affiliation(s)
- Maame Akua Korsah
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia.
| | - Stuart T Johnston
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Kathryn E Tiedje
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Karen P Day
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Jennifer A Flegg
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Camelia R Walker
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
- Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia
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2
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Musa SS, Zhao S, Abdulrashid I, Qureshi S, Colubri A, He D. Evaluating the spike in the symptomatic proportion of SARS-CoV-2 in China in 2022 with variolation effects: a modeling analysis. Infect Dis Model 2024; 9:601-617. [PMID: 38558958 PMCID: PMC10978539 DOI: 10.1016/j.idm.2024.02.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Revised: 02/20/2024] [Accepted: 02/24/2024] [Indexed: 04/04/2024] Open
Abstract
Despite most COVID-19 infections being asymptomatic, mainland China had a high increase in symptomatic cases at the end of 2022. In this study, we examine China's sudden COVID-19 symptomatic surge using a conceptual SIR-based model. Our model considers the epidemiological characteristics of SARS-CoV-2, particularly variolation, from non-pharmaceutical intervention (facial masking and social distance), demography, and disease mortality in mainland China. The increase in symptomatic proportions in China may be attributable to (1) higher sensitivity and vulnerability during winter and (2) enhanced viral inhalation due to spikes in SARS-CoV-2 infections (high transmissibility). These two reasons could explain China's high symptomatic proportion of COVID-19 in December 2022. Our study, therefore, can serve as a decision-support tool to enhance SARS-CoV-2 prevention and control efforts. Thus, we highlight that facemask-induced variolation could potentially reduces transmissibility rather than severity in infected individuals. However, further investigation is required to understand the variolation effect on disease severity.
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Affiliation(s)
- Salihu S. Musa
- Department of Genomics and Computational Biology, University of Massachusetts Chan Medical School, Worcester, MA, 01605, USA
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong SAR, China
- Department of Mathematics, Aliko Dangote University of Science and Technology, Kano, Nigeria
| | - Shi Zhao
- School of Public Health, Tianjin Medical University, Tianjin, 300070, China
| | - Ismail Abdulrashid
- School of Finance and Operations Management, The University of Tulsa, 800 South Tucker Dr., Tulsa, OK, 74104, USA
| | - Sania Qureshi
- Department of Basic Sciences and Related Studies, Mehran University of Engineering and Tech., Jamshoro, Pakistan
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Andrés Colubri
- Department of Genomics and Computational Biology, University of Massachusetts Chan Medical School, Worcester, MA, 01605, USA
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong SAR, China
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3
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Korsah MA, Johnston ST, Tiedje KE, Day KP, Flegg JA, Walker CR. Mathematical assessment of the role of intervention programs for malaria control. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2023:2023.12.18.23300185. [PMID: 38196597 PMCID: PMC10775318 DOI: 10.1101/2023.12.18.23300185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.
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Affiliation(s)
- Maame Akua Korsah
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Stuart T Johnston
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Kathryn E Tiedje
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Karen P Day
- Department of Microbiology and Immunology, Bio21 Institute and Peter Doherty Institute, The University of Melbourne, Melbourne, Australia
| | - Jennifer A Flegg
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
| | - Camelia R Walker
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
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4
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Zhang T, Zhang Z, Yu Z, Huang Q, Gao D. Effects of behaviour change on HFMD transmission. JOURNAL OF BIOLOGICAL DYNAMICS 2023; 17:2244968. [PMID: 37581613 DOI: 10.1080/17513758.2023.2244968] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Accepted: 08/01/2023] [Indexed: 08/16/2023]
Abstract
We propose a hand, foot and mouth disease (HFMD) transmission model for children with behaviour change and imperfect quarantine. The symptomatic and quarantined states obey constant behaviour change while others follow variable behaviour change depending on the numbers of new and recent infections. The basic reproduction number R 0 of the model is defined and shown to be a threshold for disease persistence and eradication. Namely, the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 whereas the disease persists and there is a unique endemic equilibrium otherwise. By fitting the model to weekly HFMD data of Shanghai in 2019, the reproduction number is estimated at 2.41. Sensitivity analysis for R 0 shows that avoiding contagious contacts and implementing strict quarantine are essential to lower HFMD persistence. Numerical simulations suggest that strong behaviour change not only reduces the peak size and endemic level dramatically but also impairs the role of asymptomatic transmission.
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Affiliation(s)
- Tongrui Zhang
- Department of Mathematics, Shanghai Normal University, Shanghai, People's Republic of China
| | - Zhijie Zhang
- Department of Epidemiology and Health Statistics, Fudan University, Shanghai, People's Republic of China
| | - Zhiyuan Yu
- Department of Biology, Case Western Reserve University, Cleveland, OH, USA
| | - Qimin Huang
- Department of Mathematical and Computational Sciences, The College of Wooster, Wooster, OH, USA
| | - Daozhou Gao
- Department of Mathematics, Shanghai Normal University, Shanghai, People's Republic of China
- Department of Mathematics and Statistics, Cleveland State University, Cleveland, OH, USA
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5
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Ibrahim A, Humphries UW, Ngiamsunthorn PS, Baba IA, Qureshi S, Khan A. Modeling the dynamics of COVID-19 with real data from Thailand. Sci Rep 2023; 13:13082. [PMID: 37567888 PMCID: PMC10421938 DOI: 10.1038/s41598-023-39798-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Accepted: 07/31/2023] [Indexed: 08/13/2023] Open
Abstract
In recent years, COVID-19 has evolved into many variants, posing new challenges for disease control and prevention. The Omicron variant, in particular, has been found to be highly contagious. In this study, we constructed and analyzed a mathematical model of COVID-19 transmission that incorporates vaccination and three different compartments of the infected population: asymptomatic [Formula: see text], symptomatic [Formula: see text], and Omicron [Formula: see text]. The model is formulated in the Caputo sense, which allows for fractional derivatives that capture the memory effects of the disease dynamics. We proved the existence and uniqueness of the solution of the model, obtained the effective reproduction number, showed that the model exhibits both endemic and disease-free equilibrium points, and showed that backward bifurcation can occur. Furthermore, we documented the effects of asymptomatic infected individuals on the disease transmission. We validated the model using real data from Thailand and found that vaccination alone is insufficient to completely eradicate the disease. We also found that Thailand must monitor asymptomatic individuals through stringent testing to halt and subsequently eradicate the disease. Our study provides novel insights into the behavior and impact of the Omicron variant and suggests possible strategies to mitigate its spread.
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Affiliation(s)
- Alhassan Ibrahim
- Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand
- Department of Mathematical Sciences, Bayero University, Kano, Nigeria
| | - Usa Wannasingha Humphries
- Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand.
| | - Parinya Sa Ngiamsunthorn
- Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand
| | - Isa Abdullahi Baba
- Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand
- Department of Mathematical Sciences, Bayero University, Kano, Nigeria
| | - Sania Qureshi
- Department of mathematics, Near East University TRNC, Mersin 10, Turkey
- Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, 76062, Pakistan
| | - Amir Khan
- Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, kpk, Pakistan
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6
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Sun M, Fu X. Competitive dual-strain SIS epidemiological models with awareness programs in heterogeneous networks: two modeling approaches. J Math Biol 2023; 87:14. [PMID: 37336794 DOI: 10.1007/s00285-023-01945-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2021] [Revised: 04/06/2023] [Accepted: 06/02/2023] [Indexed: 06/21/2023]
Abstract
Epidemic diseases and media campaigns are closely associated with each other. Considering most epidemics have multiple pathogenic strains, in this paper, we take the lead in proposing two multi-strain SIS epidemic models in heterogeneous networks incorporating awareness programs due to media. For the first model, we assume that the transmission rates for strain 1 and strain 2 depend on the level of awareness campaigns. For the second one, we further suppose that awareness divides susceptible population into two different subclasses. After defining the basic reproductive numbers for the whole model and each strain, we obtain the analytical conditions that determine the extinction, coexistence and absolute dominance of two strains. Moreover, we also formulate its optimal control problem and identify an optimal implementation pair of awareness campaigns using optimal control theory. Given the complexity of the second model, we use the numerical simulations to visualize its different types of dynamical behaviors. Through theoretical and numerical analysis of these two models, we discover some new phenomena. For example, during the persistence analysis of the first model, we find that the characteristic polynomials of two boundary equilibria may have a pair of pure imaginary roots, implying that Hopf bifurcation and periodic solutions may appear. Most strikingly, multistability occurs in the second model and the growth rate of awareness programs (triggered by the infection prevalence) has a multistage impact on the final size of two strains. The numerical results suggest that the spread of a two-strain epidemic can be controlled (even be eradicated) by taking the measures of enhancing awareness transmission, reducing memory fading of aware individuals and ensuring high-level influx and rapid growth of awareness programs appropriately.
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Affiliation(s)
- Mengfeng Sun
- Department of Mathematics, Shanghai University, Shanghai, 200444, China.
| | - Xinchu Fu
- Department of Mathematics, Shanghai University, Shanghai, 200444, China
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7
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Ibrahim A, Humphries UW, Khan A, Iliyasu Bala S, Baba IA, Rihan FA. COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines. Vaccines (Basel) 2022; 11:vaccines11010003. [PMID: 36679848 PMCID: PMC9861103 DOI: 10.3390/vaccines11010003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Revised: 12/12/2022] [Accepted: 12/15/2022] [Indexed: 12/24/2022] Open
Abstract
It is a known fact that there are a particular set of people who are at higher risk of getting COVID-19 infection. Typically, these high-risk individuals are recommended to take more preventive measures. The use of non-pharmaceutical interventions (NPIs) and the vaccine are playing a major role in the dynamics of the transmission of COVID-19. We propose a COVID-19 model with high-risk and low-risk susceptible individuals and their respective intervention strategies. We find two equilibrium solutions and we investigate the basic reproduction number. We also carry out the stability analysis of the equilibria. Further, this model is extended by considering the vaccination of some non-vaccinated individuals in the high-risk population. Sensitivity analyses and numerical simulations are carried out. From the results, we are able to obtain disease-free and endemic equilibrium solutions by solving the system of equations in the model and show their global stabilities using the Lyapunov function technique. The results obtained from the sensitivity analysis shows that reducing the hospitals' imperfect efficacy can have a positive impact on the control of COVID-19. Finally, simulations of the extended model demonstrate that vaccination could adequately control or eliminate COVID-19.
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Affiliation(s)
- Alhassan Ibrahim
- Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
- Department of Mathematical Sciences, Bayero University, Kano Kano 700006, Nigeria
| | - Usa Wannasingha Humphries
- Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
- Correspondence:
| | - Amir Khan
- Department of Mathematics and Statistics, University of Swat, Khyber 01923, Pakistan
| | - Saminu Iliyasu Bala
- Department of Mathematical Sciences, Bayero University, Kano Kano 700006, Nigeria
| | - Isa Abdullahi Baba
- Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
- Department of Mathematical Sciences, Bayero University, Kano Kano 700006, Nigeria
| | - Fathalla A. Rihan
- Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, United Arab Emirates
- Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt
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8
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Wang J. Mathematical Models for Cholera Dynamics-A Review. Microorganisms 2022; 10:microorganisms10122358. [PMID: 36557611 PMCID: PMC9783556 DOI: 10.3390/microorganisms10122358] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Revised: 11/27/2022] [Accepted: 11/28/2022] [Indexed: 11/30/2022] Open
Abstract
Cholera remains a significant public health burden in many countries and regions of the world, highlighting the need for a deeper understanding of the mechanisms associated with its transmission, spread, and control. Mathematical modeling offers a valuable research tool to investigate cholera dynamics and explore effective intervention strategies. In this article, we provide a review of the current state in the modeling studies of cholera. Starting from an introduction of basic cholera transmission models and their applications, we survey model extensions in several directions that include spatial and temporal heterogeneities, effects of disease control, impacts of human behavior, and multi-scale infection dynamics. We discuss some challenges and opportunities for future modeling efforts on cholera dynamics, and emphasize the importance of collaborations between different modeling groups and different disciplines in advancing this research area.
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Affiliation(s)
- Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
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9
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Musa SS, Yusuf A, Bakare EA, Abdullahi ZU, Adamu L, Mustapha UT, He D. Unravelling the dynamics of Lassa fever transmission with differential infectivity: Modeling analysis and control strategies. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:13114-13136. [PMID: 36654038 DOI: 10.3934/mbe.2022613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Epidemic models have been broadly used to comprehend the dynamic behaviour of emerging and re-emerging infectious diseases, predict future trends, and assess intervention strategies. The symptomatic and asymptomatic features and environmental factors for Lassa fever (LF) transmission illustrate the need for sophisticated epidemic models to capture more vital dynamics and forecast trends of LF outbreaks within countries or sub-regions on various geographic scales. This study proposes a dynamic model to examine the transmission of LF infection, a deadly disease transmitted mainly by rodents through environment. We extend prior LF models by including an infectious stage to mild and severe as well as incorporating environmental contributions from infected humans and rodents. For model calibration and prediction, we show that the model fits well with the LF scenario in Nigeria and yields remarkable prediction results. Rigorous mathematical computation divulges that the model comprises two equilibria. That is disease-free equilibrium, which is locally-asymptotically stable (LAS) when the basic reproduction number, $ {\mathcal{R}}_{0} $, is $ < 1 $; and endemic equilibrium, which is globally-asymptotically stable (GAS) when $ {\mathcal{R}}_{0} $ is $ > 1 $. We use time-dependent control strategy by employing Pontryagin's Maximum Principle to derive conditions for optimal LF control. Furthermore, a partial rank correlation coefficient is adopted for the sensitivity analysis to obtain the model's top rank parameters requiring precise attention for efficacious LF prevention and control.
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Affiliation(s)
- Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
- Department of Mathematics, Kano University of Science and Technology, Wudil, Kano, Nigeria
| | - Abdullahi Yusuf
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
| | - Emmanuel A Bakare
- Department of Mathematics, Federal University Oye Ekiti, Ekiti, Nigeria
- Biomathematics and Applied Mathematical Modelling Research Group, Federal University Oye Ekiti, Ekiti, Nigeria
| | - Zainab U Abdullahi
- Department of Biological Sciences, Federal University Dutsin-Ma, Katsina, Nigeria
| | - Lukman Adamu
- Department of Mathematical Sciences, Faculty of Science, University of Maiduguri, Nigeria
| | - Umar T Mustapha
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
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10
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Gupta RK, Pal S, Misra AK. Modeling the impact of precautionary measures and sanitation practices broadcasted through media on the dynamics of bacterial diseases. MODELING EARTH SYSTEMS AND ENVIRONMENT 2022; 9:397-412. [PMID: 36059593 PMCID: PMC9420191 DOI: 10.1007/s40808-022-01469-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 07/13/2022] [Indexed: 06/15/2023]
Abstract
The media has a significant contribution in spreading awareness by broadcasting various programs about prevalent diseases in the society along with the role of providing information, feeding news and educating a large mass. In this paper, the effect of media programs promoting precautionary measures and sanitation practices to control the bacterial infection in the community is modeled and analyzed considering the number of media programs as a dynamical variable. In the modeling phenomena, human population is partitioned into three classes; susceptible, infected and recovered. The disease is supposed to spread by direct contact of susceptible with infected individuals and indirectly by the ingestion of bacteria present in the environment. The growth in the media programs is considered proportional to the size of infected population and the impact of these programs on the indirect disease transmission rate and bacteria shedding rate by infected individuals is also considered. The feasibility of equilibria and their stability conditions are obtained. Model analysis reveals that broadcasting media programs and increasing its effectiveness shrink the size of infected class and control the spread of disease to a large extent.
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Affiliation(s)
- Rabindra Kumar Gupta
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221 005 India
- Department of Mathematics, Butwal Multiple Campus, T.U., Butwal, Lumbini 284403 Nepal
| | - Soumitra Pal
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221 005 India
| | - A. K. Misra
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221 005 India
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11
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Alqahtani RT, Musa SS, Yusuf A. Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization. RESULTS IN PHYSICS 2022; 39:105715. [PMID: 35720511 PMCID: PMC9192123 DOI: 10.1016/j.rinp.2022.105715] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 06/02/2022] [Accepted: 06/07/2022] [Indexed: 05/12/2023]
Abstract
The coronavirus disease 2019 (COVID-19) is caused by a newly emerged virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), transmitted through air droplets from an infected person. However, other transmission routes are reported, such as vertical transmission. Here, we propose an epidemic model that considers the combined effect of vertical transmission, vaccination and hospitalization to investigate the dynamics of the virus's dissemination. Rigorous mathematical analysis of the model reveals that two equilibria exist: the disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number ( R 0 ) is less than 1 (unstable otherwise), and an endemic equilibrium, which is globally asymptotically stable when R 0 > 1 under certain conditions, implying the plausibility of the disease to spread and cause large outbreaks in a community. Moreover, we fit the model using the Saudi Arabia cases scenario, which designates the incidence cases from the in-depth surveillance data as well as displays the epidemic trends in Saudi Arabia. Through Caputo fractional-order, simulation results are provided to show dynamics behaviour on the model parameters. Together with the non-integer order variant, the proposed model is considered to explain various dynamics features of the disease. Further numerical simulations are carried out using an efficient numerical technique to offer additional insight into the model's dynamics and investigate the combined effect of vaccination, vertical transmission, and hospitalization. In addition, a sensitivity analysis is conducted on the model parameters against the R 0 and infection attack rate to pinpoint the most crucial parameters that should be emphasized in controlling the pandemic effectively. Finally, the findings suggest that adequate vaccination coupled with basic non-pharmaceutical interventions are crucial in mitigating disease incidences and deaths.
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Affiliation(s)
- Rubayyi T Alqahtani
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
| | - Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
- Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey
| | - Abdullahi Yusuf
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
- Department of Mathematics, Federal University Dutse, Jigawa, Nigeria
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12
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Musa SS, Yusuf A, Zhao S, Abdullahi ZU, Abu-Odah H, Saad FT, Adamu L, He D. Transmission dynamics of COVID-19 pandemic with combined effects of relapse, reinfection and environmental contribution: A modeling analysis. RESULTS IN PHYSICS 2022; 38:105653. [PMID: 35664991 PMCID: PMC9148429 DOI: 10.1016/j.rinp.2022.105653] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Revised: 05/20/2022] [Accepted: 05/23/2022] [Indexed: 05/25/2023]
Abstract
Reinfection and reactivation of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have recently raised public health pressing concerns in the fight against the current pandemic globally. In this study, we propose a new dynamic model to study the transmission of the coronavirus disease 2019 (COVID-19) pandemic. The model incorporates possible relapse, reinfection and environmental contribution to assess the combined effects on the overall transmission dynamics of SARS-CoV-2. The model's local asymptotic stability is analyzed qualitatively. We derive the formula for the basic reproduction number (R 0 ) and final size epidemic relation, which are vital epidemiological quantities that are used to reveal disease transmission status and guide control strategies. Furthermore, the model is validated using the COVID-19 reported situations in Saudi Arabia. Moreover, sensitivity analysis is examined by implementing a partial rank correlation coefficient technique to obtain the ultimate rank model parameters to control or mitigate the pandemic effectively. Finally, we employ a standard Euler technique for numerical simulations of the model to elucidate the influence of some crucial parameters on the overall transmission dynamics. Our results highlight that contact rate, hospitalization rate, and reactivation rate are the fundamental parameters that need particular emphasis for the prevention, mitigation and control.
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Affiliation(s)
- Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
- Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
| | - Abdullahi Yusuf
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Shi Zhao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China
| | - Zainab U Abdullahi
- Department of Biological Sciences, Federal University Dutsin-Ma, Katsina, Nigeria
| | - Hammoda Abu-Odah
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
- Nursing and Health Sciences Department, University College of Applied Sciences, Gaza, Palestine
| | | | - Lukman Adamu
- Department of Mathematical Sciences, University of Maiduguri, Nigeria
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
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13
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Kimball P, Levenson J, Moore A, Rychtar J, Taylor D. An ODE model of yaws elimination in Lihir Island, Papua New Guinea. PeerJ 2022; 10:e13018. [PMID: 35317072 PMCID: PMC8934533 DOI: 10.7717/peerj.13018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 02/06/2022] [Indexed: 01/11/2023] Open
Abstract
Yaws is a chronic infection that affects mainly the skin, bone and cartilage and spreads mostly between children. The new approval of a medication as treatment in 2012 has revived eradication efforts and now only few known localized foci of infection remain. The World Health Organization strategy mandates an initial round of total community treatment (TCT) with single-dose azithromycin followed either by further TCT or by total targeted treatment (TTT), an active case-finding and treatment of cases and their contacts. We develop the compartmental ODE model of yaws transmission and treatment for these scenarios. We solve for disease-free and endemic equilibria and also perform the stability analysis. We calibrate the model and validate its predictions on the data from Lihir Island in Papua New Guinea. We demonstrate that TTT strategy is efficient in preventing outbreaks but, due to the presence of asymptomatic latent cases, TTT will not eliminate yaws within a reasonable time frame. To achieve the 2030 eradication target, TCT should be applied instead.
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Affiliation(s)
- Presley Kimball
- Department of Mathematics, Creighton University, Omaha, NE, United States of America
| | - Jacob Levenson
- Department of Mathematics, Washington and Lee University, Lexington, VA, United States of America
| | - Amy Moore
- Department of Mathematics and Statistics, Elon University, Elon, NC, United States of America
| | - Jan Rychtar
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States of America
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States of America
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14
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Stability Analysis and Optimal Control of a Fractional Cholera Epidemic Model. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030157] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
In this paper, a fractional model for the transmission dynamics of cholera was developed. In invariant regions of the model, solutions were generated. Disease-free and endemic equilibrium points were obtained. The basic reproduction number was evaluated, and the sensitivity analysis was performed. Under the support of Pontryagin’s maximum principle, the fractional order optimal control was obtained. Furthermore, an optimal strategy was discussed, which minimized the total number of infected individuals and the costs associated with control. Treatment, vaccination, and awareness programs were regarded as three means to reduce the number of infected. Finally, numerical simulations and cost-effectiveness analysis were presented to show the result that the best strategy was the combination of treatment and awareness programs.
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15
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TIWARI PANKAJKUMAR, RAI RAJANISHKUMAR, GUPTA RABINDRAKUMAR, MARTCHEVA MAIA, MISRA ARVINDKUMAR. Modeling the Control of Bacterial Disease by Social Media Advertisements: Effects of Awareness and Sanitation. J BIOL SYST 2022. [DOI: 10.1142/s0218339022500024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Media impact has significant effect on reducing the disease prevalence, meanwhile sanitation and awareness can control the epidemic by reducing the growth rate of bacteria and direct contacts with infected individuals. In this paper, we investigate the impacts of media and sanitation coverage on the dynamics of epidemic outbreak. We observe that the growth rate of social media advertisements carries out a destabilizing role, while the system regains stability if the baseline number of social media advertisements exceeds a certain threshold. The dissemination of awareness among susceptibles first destabilizes and then stabilizes the system. The disease can be wiped out if the baseline level of awareness or the rate of spreading global information about the disease and its preventive measures is too high. We obtain an explicit expression for the basic reproduction number [Formula: see text] and show that [Formula: see text] leads to the total eradication of infection from the region. To capture a more realistic scenario, we construct the forced delay model by seasonally varying the growth rate of social media advertisements and incorporating the time lag involved in reporting of total infective cases to the policy makers. Seasonal pattern in the growth rate of social media advertisements adds complexity to the system by inducing chaotic oscillations. For gradual increase in the delay in reported cases of infected individuals, the nonautonomous system switches finitely many times between periodic and chaotic states.
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Affiliation(s)
- PANKAJ KUMAR TIWARI
- Department of Basic Science and Humanities, Indian Institute of Information Technology, Bhagalpur 813210, India
| | - RAJANISH KUMAR RAI
- Department of Mathematics, Jaypee Institute of Information Technology, Noida, Uttar Pradesh 201301, India
| | - RABINDRA KUMAR GUPTA
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
| | - MAIA MARTCHEVA
- Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
| | - ARVIND KUMAR MISRA
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
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16
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Yang C, Wang J. Transmission rates and environmental reservoirs for COVID-19 - a modeling study. JOURNAL OF BIOLOGICAL DYNAMICS 2021; 15:86-108. [PMID: 33402047 PMCID: PMC7793558 DOI: 10.1080/17513758.2020.1869844] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Accepted: 12/17/2020] [Indexed: 05/20/2023]
Abstract
The coronavirus disease 2019 (COVID-19) remains a global pandemic at present. Although the human-to-human transmission route for this disease has been well established, its transmission mechanism is not fully understood. In this paper, we propose a mathematical model for COVID-19 which incorporates multiple transmission pathways and which employs time-dependent transmission rates reflecting the impact of disease prevalence and outbreak control. Applying this model to a retrospective study based on publicly reported data in China, we argue that the environmental reservoirs play an important role in the transmission and spread of the coronavirus. This argument is supported by our data fitting and numerical simulation results for the city of Wuhan, for the provinces of Hubei and Guangdong, and for the entire country of China.
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Affiliation(s)
- Chayu Yang
- Department of Mathematics, University of Florida Gainesville, FL 32611, USA
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
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17
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Dureab F, Al-Qadasi Y, Nasr H, Al-Zumair M, Al-Mahbashi T. Knowledge on and preventive practices of cholera in Al-Mahweet - Yemen, 2018: a cross-sectional study. JOURNAL OF WATER AND HEALTH 2021; 19:1002-1013. [PMID: 34874906 DOI: 10.2166/wh.2021.139] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Yemen has experienced one of the world's worst cholera outbreaks in the recent history of cholera records. This study aims to identify knowledge and practices among people of Al-Mahweet governorate toward cholera infection, which can play a critical role in reducing cholera morbidity and shaping the public health response. A cross-sectional study was conducted in an area of high cholera prevalence in 2018 using structured questionnaires. Most community respondents were able to correctly identify the symptoms and risk factors of cholera. While 65% of the respondents in this study knew that proper disposal of human waste is an essential measure of cholera prevention, only 11% of the respondents knew that proper washing of fruits and vegetables lowers the risk of cholera infection. About 62.5% of households did not treat water for safe drinking. Water was scarce in about 30% of households and near-home defecation was observed in about 23%. In conclusion, this study reveals several gaps in different aspects of hygienic and preventive practices including water treatment, waste disposal, and defecation practices. Cholera response should contain comprehensive health promotion interventions to improve the public's knowledge and enhance healthy practices. Stakeholders should support communities with sustainable water and sanitation systems.
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Affiliation(s)
- Fekri Dureab
- Heidelberg Institute of Global Health, Uniklinikum Heidelberg 69115, Germany; IRIA, Akkon-Hochschule für Humanwissenschaften, Berlin, 12099, Germany
| | - Yasameen Al-Qadasi
- Yemeni Public Health Consultant, 2011 VN, Haarlem, The Netherlands E-mail:
| | - Hani Nasr
- Charite Universitätsmedizin-Berlin, Berlin, Germany
| | - Marwah Al-Zumair
- Heidelberg Institute of Global Health, Uniklinikum Heidelberg 69115, Germany; IRIA, Akkon-Hochschule für Humanwissenschaften, Berlin, 12099, Germany
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18
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Zewdie AD, Gakkhar S. An epidemic model with transport-related infection incorporating awareness and screening. JOURNAL OF APPLIED MATHEMATICS & COMPUTING 2021; 68:3107-3146. [PMID: 34751214 PMCID: PMC8565863 DOI: 10.1007/s12190-021-01653-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2021] [Revised: 10/20/2021] [Accepted: 10/21/2021] [Indexed: 06/13/2023]
Abstract
In this paper, an SWEIQR epidemic model with transport-related infection is proposed. The model considers inter-patch travel with entry-departure screening. The reproduction number, R ed ϕ , is computed and analyzed with respect to awareness and screening parameters. The analytic computations show that the disease-free equilibrium in the absence of travel is globally asymptotically stable when R ω ≤ 1 and unstable otherwise. The trans-critical bifurcation occurs at R ω = 1 and the locally stable endemic equilibrium point appears if R ω > 1 near to R ω = 1 . The numerical simulations are performed to verify the analytical computation and explore the dynamic behavior with respect to different model parameters. The result shows that disseminating awareness through the population reduces the spread of disease. Furthermore, the full model results show that the departure screening may reduce the spread of disease in each patch.
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Affiliation(s)
- Assefa Denekew Zewdie
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667 Uttarakhand India
- Department of Mathematics, Debre Tabor University, Debre Tabor, Amhara Ethiopia
| | - Sunita Gakkhar
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667 Uttarakhand India
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19
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Musa SS, Baba IA, Yusuf A, Sulaiman TA, Aliyu AI, Zhao S, He D. Transmission dynamics of SARS-CoV-2: A modeling analysis with high-and-moderate risk populations. RESULTS IN PHYSICS 2021; 26:104290. [PMID: 34026471 PMCID: PMC8131571 DOI: 10.1016/j.rinp.2021.104290] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Revised: 04/30/2021] [Accepted: 05/01/2021] [Indexed: 05/03/2023]
Abstract
Nigeria is second to South Africa with the highest reported cases of COVID-19 in sub-Saharan Africa. In this paper, we employ an SEIR-based compartmental model to study and analyze the transmission dynamics of SARS-CoV-2 outbreaks in Nigeria. The model incorporates different group of populations (that is, high- and- moderate risk populations) and is use to investigate the influence on each population on the overall transmission dynamics.The model, which is fitted well to the data, is qualitatively analyzed to evaluate the impacts of different schemes for controlstrategies. Mathematical analysis reveals that the model has two equilibria; i.e., disease-free equilibrium (DFE) which is local asymptotic stability (LAS) if the basic reproduction number (R 0 ) is less than 1; and unstable forR 0 > 1 , and an endemic equilibrium (EE) which is globally asymptotic stability (LAS) wheneverR 0 > 1 . Furthermore, we find that the model undergoes a phenomenon of backward bifurcation (BB, a coexistence of stable DFE and stable EE even if theR 0 < 1 ). We employ Partial Rank Correlation coefficients (PRCCs) for sensitivity analyses to evaluate the model's parameters. Our results highlight that proper surveillance, especially movement of individuals from high risk to moderate risk population, testing, as well as imposition of other NPIs measures are vital strategies for mitigating the COVID-19 epidemic in Nigeria. Besides, in the absence of an exact solution for the proposed model, we solve the model with the well-known ODE45 numerical solver and the effective numerical schemes such as Euler (EM), Runge-Kutta of order 2 (RK-2), and Runge-Kutta of order 4 (RK-4) in order to establish approximate solutions and to show the physical features of the model. It has been shown that these numerical schemes are very effective and efficient to establish superb approximate solutions for differential equations.
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Affiliation(s)
- Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong
- Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
| | - Isa A Baba
- Department of Mathematics, Bayero University Kano, Nigeria
| | - Abdullahi Yusuf
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Tukur A Sulaiman
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Aliyu I Aliyu
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Shi Zhao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong
- CUHK Shenzhen Research Institute, Shenzhen, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong
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20
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Giambiagi Ferrari C, Pinasco JP, Saintier N. Coupling Epidemiological Models with Social Dynamics. Bull Math Biol 2021; 83:74. [PMID: 34008047 PMCID: PMC8130810 DOI: 10.1007/s11538-021-00910-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2020] [Accepted: 05/05/2021] [Indexed: 11/25/2022]
Abstract
In this work we study a Susceptible-Infected-Susceptible model coupled with a continuous opinion dynamics model. We assume that each individual can take measures to reduce the probability of contagion, and the level of effort each agent applies can change due to social interactions. We propose simple rules to model the propagation of behaviors that modify the level of effort, and analyze their impact on the dynamics of the disease. We derive a two dimensional set of ordinary differential equations describing the dynamic of the proportion of the number of infected individuals and the mean value of the effort parameter, and analyze the equilibria of the system. The stability of the endemic phase and disease free equilibria depends only on the mean value of the levels of efforts, and not on the initial distribution of levels of effort.
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Affiliation(s)
- Carlo Giambiagi Ferrari
- IMAS, Instituto de Investigaciones Matemáticas Luis A. Santaló, CONICET and Universidad de Buenos Aires, Av Cantilo s/n, Ciudad Universitaria, 1428, Buenos Aires, Argentina
| | - Juan Pablo Pinasco
- IMAS, Instituto de Investigaciones Matemáticas Luis A. Santaló, CONICET and Universidad de Buenos Aires, Av Cantilo s/n, Ciudad Universitaria, 1428, Buenos Aires, Argentina.
| | - Nicolas Saintier
- Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Av Cantilo s/n, Ciudad Universitaria, 1428, Buenos Aires, Argentina
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21
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Yang C, Wang J. COVID-19 and underlying health conditions: A modeling investigation. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:3790-3812. [PMID: 34198413 PMCID: PMC8359646 DOI: 10.3934/mbe.2021191] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We propose a mathematical model based on a system of differential equations, which incorporates the impact of the chronic health conditions of the host population, to investigate the transmission dynamics of COVID-19. The model divides the total population into two groups, depending on whether they have underlying conditions, and describes the disease transmission both within and between the groups. As an application of this model, we perform a case study for Hamilton County, the fourth-most populous county in the US state of Tennessee and a region with high prevalence of chronic conditions. Our data fitting and simulation results quantify the high risk of COVID-19 for the population group with underlying health conditions. The findings suggest that weakening the disease transmission route between the exposed and susceptible individuals, including the reduction of the between-group contact, would be an effective approach to protect the most vulnerable people in this population group.
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Affiliation(s)
- Chayu Yang
- Department of Mathematics, University of Florida, Gainesville, FL 32607, USA
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Ave., Chattanooga, TN 37403, USA
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22
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Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics. J Math Biol 2021; 82:48. [PMID: 33830353 DOI: 10.1007/s00285-021-01603-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 11/20/2020] [Accepted: 03/29/2021] [Indexed: 10/21/2022]
Abstract
Seasonal variation affects the dynamics of many infectious diseases including influenza, cholera and malaria. The time when infectious individuals are first introduced into a population is crucial in predicting whether a major disease outbreak occurs. In this investigation, we apply a time-nonhomogeneous stochastic process for a cholera epidemic with seasonal periodicity and a multitype branching process approximation to obtain an analytical estimate for the probability of an outbreak. In particular, an analytic estimate of the probability of disease extinction is shown to satisfy a system of ordinary differential equations which follows from the backward Kolmogorov differential equation. An explicit expression for the mean (resp. variance) of the first extinction time given an extinction occurs is derived based on the analytic estimate for the extinction probability. Our results indicate that the probability of a disease outbreak, and mean and standard derivation of the first time to disease extinction are periodic in time and depend on the time when the infectious individuals or free-living pathogens are introduced. Numerical simulations are then carried out to validate the analytical predictions using two examples of the general cholera model. At the end, the developed theoretical results are extended to more general models of infectious diseases.
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23
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24
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Yang C, Wang J. Modeling the transmission of COVID-19 in the US - A case study. Infect Dis Model 2020; 6:195-211. [PMID: 33506152 PMCID: PMC7809398 DOI: 10.1016/j.idm.2020.12.006] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 12/20/2020] [Indexed: 01/03/2023] Open
Abstract
We propose a mathematical model to investigate the transmission dynamics of COVID-19. The model incorporates both human-to-human and environment-to-human transmission pathways, and employs different transmission rates to represent the epidemiological characteristics at different time periods. Using this model and publicly reported data, we perform a case study for Hamilton County, the fourth-most populous county in the state of Tennessee and a region that could represent the typical situation of COVID-19 in the United States (US). Our data fitting and simulation results show that the environment may play an important role in the transmission and spread of the coronavirus. In addition, we numerically simulate a range of epidemic scenarios and make near-term forecasts on the development and trend of COVID-19 in Hamilton County.
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Affiliation(s)
- Chayu Yang
- Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA
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25
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BROWN MARGARET, JIANG MIKO, YANG CHAYU, WANG JIN. MODELING CHOLERA TRANSMISSION UNDER DISEASE CONTROL MEASURES. J BIOL SYST 2020. [DOI: 10.1142/s0218339021400015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We present a new mathematical model to investigate the transmission dynamics of cholera under disease control measures that include education programs and water sanitation. The model incorporates the impact of education programs into the disease transmission rates and that of water sanitation into the environmental pathogen dynamics. We conduct a detailed analysis to the autonomous system of the model and establish the local and global stabilities of its equilibria that characterize the threshold dynamics of cholera. We then perform an optimal control study on the general model with time-dependent controls and explore effective approaches to implement the education programs and water sanitation while balancing their costs. Our analysis and simulation highlight the complex interaction among the direct and indirect transmission pathways of the disease, the intrinsic growth of the environmental pathogen and the impact of multiple control measures, and their roles in collectively shaping the transmission dynamics of cholera.
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Affiliation(s)
- MARGARET BROWN
- Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
| | - MIKO JIANG
- Department of Mathematics, Brandeis University, Waltham, MA 02453, USA
| | - CHAYU YANG
- Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
| | - JIN WANG
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
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26
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Modeling the 2014-2015 Ebola Virus Disease Outbreaks in Sierra Leone, Guinea, and Liberia with Effect of High- and Low-risk Susceptible Individuals. Bull Math Biol 2020; 82:102. [PMID: 32734342 DOI: 10.1007/s11538-020-00779-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2019] [Accepted: 07/14/2020] [Indexed: 10/23/2022]
Abstract
Ebola virus disease (EVD) is a rare but fatal disease of humans and other primates caused by Ebola viruses. Study shows that the 2014-2015 EVD outbreak causes more than 10,000 deaths. In this paper, we propose and analyze a deterministic model to study the transmission dynamics of EVD in Sierra Leone, Guinea, and Liberia. Our analyses show that the model has two equilibria: (1) the disease-free equilibrium (DFE) which is locally asymptotically stable when the basic reproduction number ([Formula: see text]) is less than unity and unstable if it is greater than one, and (2) an endemic equilibrium (EE) which is globally asymptotically stable when [Formula: see text] is greater than unity. Furthermore, the backward bifurcation occurs, a coexistence between a stale DFE and a stable EE even if the [Formula: see text] is less than unity, which makes the disease control more strenuous and would depend on the initial size of subpopulation. By fitting to reported Ebola cases from Sierra Leone, Guinea, and Liberia in 2014-2015, our model has captured the epidemic patterns in all three countries and shed light on future Ebola control and prevention strategies.
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27
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Mathematical Analysis of the Ross-Macdonald Model with Quarantine. Bull Math Biol 2020; 82:47. [PMID: 32242279 PMCID: PMC7117789 DOI: 10.1007/s11538-020-00723-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2019] [Accepted: 03/19/2020] [Indexed: 11/23/2022]
Abstract
People infected with malaria may receive less mosquito bites when they are treated in well-equipped hospitals or follow doctors’ advice for reducing exposure to mosquitoes at home. This quarantine-like intervention measure is especially feasible in countries and areas approaching malaria elimination. Motivated by mathematical models with quarantine for directly transmitted diseases, we develop a mosquito-borne disease model where imperfect quarantine is considered to mitigate the disease transmission from infected humans to susceptible mosquitoes. The basic reproduction number \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0$$\end{document}R0 is computed and the model equilibria and their stabilities are analyzed when the incidence rate is standard or bilinear. In particular, the model system may undergo a subcritical (backward) bifurcation at \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0=1$$\end{document}R0=1 when standard incidence is adopted, whereas the disease-free equilibrium is globally asymptotically stable as \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0\le 1$$\end{document}R0≤1 and the unique endemic equilibrium is locally asymptotically stable as \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0>1$$\end{document}R0>1 when the infection incidence is bilinear. Numerical simulations suggest that the quarantine strategy can play an important role in decreasing malaria transmission. The success of quarantine mainly relies on the reduction of bites on quarantined individuals.
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28
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Zhao S, Musa SS, Qin J, He D. Associations between Public Awareness, Local Precipitation, and Cholera in Yemen in 2017. Am J Trop Med Hyg 2020; 101:521-524. [PMID: 31333154 DOI: 10.4269/ajtmh.18-1016] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
In 2017-18, a large-scale cholera outbreak swept Yemen. We calculated the number of culture-confirmed cases from the suspected cases and diagnosis testing records. We estimate 184,248 confirmed cholera cases between April 2017 and the end of 2017, and the reproduction number of 2.2 with 95% CI of [2.1, 2.3] during the initial stage. We find a significantly (nonlinear) positive association between the reproduction number (R t) and precipitation, explained 13% of transmissibility changes, with one unit (mm) increment in precipitation leading to an increment of 20.1% in R t. We find a significantly (nonlinear) negative association between the R t and cumulative Google Trends index (GTI), explained 62% of transmissibility changes, with one unit increment in cumulative GTI leading to a drop of 0.03% in R t.
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Affiliation(s)
- Shi Zhao
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China.,Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Jing Qin
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
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29
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Musa SS, Zhao S, Hussaini N, Habib AG, He D. Mathematical modeling and analysis of meningococcal meningitis transmission dynamics. INT J BIOMATH 2020. [DOI: 10.1142/s1793524520500060] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Meningococcal meningitis (MCM) is one of the serious public health threats in the tropical and sub-tropical regions. In this paper, we propose an epidemic model to study the transmission dynamics of MCM with high- and low-risk susceptible populations. The model considers two different groups of susceptible individuals depending on the availability of medical resources (MR, including hospitals, health workers, etc.), which varies the infection risk. We find that the model exhibits the phenomenon of backward bifurcation (BB), which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number, [Formula: see text]. This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease. Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths, especially, in the MCM endemic regions.
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Affiliation(s)
- Salihu Sabiu Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom Hong Kong, P. R. China
- Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
| | - Shi Zhao
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom Hong Kong, P. R. China
- School of Nursing, Hong Kong Polytechnic University, Hung Hom, Hong Kong, P. R. China
- Division of Biostatistics, JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, P. R. China
| | - Nafiu Hussaini
- Department of Mathematical Sciences, Bayero University, Kano, Nigeria
| | | | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom Hong Kong, P. R. China
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30
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He D, Wang X, Gao D, Wang J. Modeling the 2016-2017 Yemen cholera outbreak with the impact of limited medical resources. J Theor Biol 2018; 451:80-85. [PMID: 29727633 DOI: 10.1016/j.jtbi.2018.04.041] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2018] [Revised: 04/28/2018] [Accepted: 04/30/2018] [Indexed: 10/17/2022]
Abstract
We present a mathematical model to investigate the transmission dynamics of the 2016-2017 Yemen cholera outbreak. Our model describes the interaction between the human hosts and the pathogenic bacteria, under the impact of limited medical resources. We fit our model to Yemen epidemic data published by the World Health Organization, at both the country and regional levels. We find that the Yemen cholera outbreak is shaped by the interplay of environmental, socioeconomic, and climatic factors. Our results suggest that improvement of the public health system and strategic implementation of control measures with respect to time and location are key to future cholera prevention and intervention in Yemen.
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Affiliation(s)
- Daihai He
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hung Hom, Hong Kong SAR, China
| | - Xueying Wang
- Department of Mathematics, Washington State University, Pullman, WA, 99164, USA
| | - Daozhou Gao
- College of Mathematics and Sciences, Shanghai Normal University, Shanghai, 200234, China
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA.
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Yang C, Posny D, Bao F, Wang J. A multi-scale cholera model linking between-host and within-host dynamics. INT J BIOMATH 2018. [DOI: 10.1142/s1793524518500341] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host level, we describe the evolution of the pathogen within the human body. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for our model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics.
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Affiliation(s)
- Chayu Yang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga TN 37403, USA
| | - Drew Posny
- NSF Center for Integrated Pest Management, North Carolina State University, Raleigh NC 27606, USA
| | - Feng Bao
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga TN 37403, USA
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga TN 37403, USA
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