1
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Wang S, Nie L. Global analysis of a diffusive Cholera model with multiple transmission pathways, general incidence and incomplete immunity in a heterogeneous environment. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:4927-4955. [PMID: 38872521 DOI: 10.3934/mbe.2024218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.
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Affiliation(s)
- Shengfu Wang
- College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
| | - Linfei Nie
- College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
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2
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Brhane KW, Ahmad AG, Hina H, Emadifar H. Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions. Sci Rep 2024; 14:4616. [PMID: 38409239 PMCID: PMC10897316 DOI: 10.1038/s41598-024-55240-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Accepted: 02/21/2024] [Indexed: 02/28/2024] Open
Abstract
A mathematical model that describes the dynamics of bacterium vibrio cholera within a fixed population considering intrinsic bacteria growth, therapeutic treatment, sanitation and vaccination rates is developed. The developed mathematical model is validated against real cholera data. A sensitivity analysis of some of the model parameters is also conducted. The intervention rates are found to be very important parameters in reducing the values of the basic reproduction number. The existence and stability of equilibrium solutions to the mathematical model are also carried out using analytical methods. The effect of some model parameters on the stability of equilibrium solutions, number of infected individuals, number of susceptible individuals and bacteria density is rigorously analyzed. One very important finding of this research work is that keeping the vaccination rate fixed and varying the treatment and sanitation rates provide a rapid decline of infection. The fourth order Runge-Kutta numerical scheme is implemented in MATLAB to generate the numerical solutions.
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Affiliation(s)
| | - Abdulaziz Garba Ahmad
- Department of Applied Mathematics, Federal University of Technology, Babura, Jigawa State, Nigeria
| | - Hina Hina
- Department of Mathematics and Statistics, Women University Swabi, Swabi, KP, Pakistan
| | - Homan Emadifar
- Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602 105, Tamil Nadu, India.
- MEU Research Unit, Middle East University, Amman, Jordan.
- Department of Mathematics, Hamedan Branch, Islamic Azad University of Hamedan, Hamadan, Iran.
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3
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Ji J, Wang H, Wang L, Ramazi P, Kong JD, Watmough J. Climate-dependent effectiveness of nonpharmaceutical interventions on COVID-19 mitigation. Math Biosci 2023; 366:109087. [PMID: 37858753 DOI: 10.1016/j.mbs.2023.109087] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2023] [Revised: 10/09/2023] [Accepted: 10/12/2023] [Indexed: 10/21/2023]
Abstract
Environmental factors have a significant impact on the transmission of infectious diseases. Existing results show that the novel coronavirus can persist outside the host. We propose a susceptible-exposed-presymptomatic-infectious-asymptomatic-recovered-susceptible (SEPIARS) model with a vaccination compartment and indirect incidence to explore the effect of environmental conditions, temperature and humidity, on the transmission of the SARS-CoV-2 virus. Using climate data and daily confirmed cases data in two Canadian cities with different atmospheric conditions, we evaluate the mortality rates of the SARS-CoV-2 virus and further estimate the transmission rates by the inverse method, respectively. The numerical results show that high temperature or humidity can be helpful in mitigating the spread of COVID-19 during the warm summer months. Our findings verify that nonpharmaceutical interventions are less effective if the virus can persist for a long time on surfaces. Based on climate data, we can forecast the transmission rate and the infection cases up to four weeks in the future by a generalized boosting machine learning model.
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Affiliation(s)
- Juping Ji
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada; Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB T6G 2R3, Canada
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada; Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB T6G 2R3, Canada.
| | - Lin Wang
- Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada
| | - Pouria Ramazi
- Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada
| | - Jude Dzevela Kong
- Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
| | - James Watmough
- Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada
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4
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Cheng X, Wang Y, Huang G. Edge-based compartmental modeling for the spread of cholera on random networks: A case study in Somalia. Math Biosci 2023; 366:109092. [PMID: 37923290 DOI: 10.1016/j.mbs.2023.109092] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Revised: 08/22/2023] [Accepted: 10/22/2023] [Indexed: 11/07/2023]
Abstract
Cholera remains a major public health problem that threatens human health worldwide and its severity is continuing. In this paper, an edge-based model for cholera transmission on random networks is proposed and investigated. The model assumes that two communities share a common water source and includes three transmission routes, namely intra- and inter-community human-to-human transmission as well as water-to-human transmission. Intra-community human-to-human contacts are modeled through a random contact network, while both inter-community and water-to-human transmission are modeled through external nodes that reach each individual in the network to the same extent. The basic reproduction number and the equations of the final epidemic size are obtained. In addition, our study considers the cholera situation in Banadir, which is one of the most severely infected regions in Somalia, during the period (2019-2021). According to the geographical location, two adjacent districts are selected and our model fits well with the real data on the monthly cumulative cholera cases of these two districts during the above-mentioned period. From the perspective of network topology, cutting off high-risk contacts by supervising, isolating, quarantining and closing places with high-degree cholera-infected individuals to reduce degree heterogeneity is an effective measure to control cholera transmission. Our findings might offer some useful insights on cholera control.
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Affiliation(s)
- Xinxin Cheng
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
| | - Yi Wang
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
| | - Gang Huang
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
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5
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Howerton E, Dahlin K, Edholm CJ, Fox L, Reynolds M, Hollingsworth B, Lytle G, Walker M, Blackwood J, Lenhart S. The effect of governance structures on optimal control of two-patch epidemic models. J Math Biol 2023; 87:74. [PMID: 37861753 PMCID: PMC10589198 DOI: 10.1007/s00285-023-02001-8] [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: 09/09/2022] [Revised: 09/07/2023] [Accepted: 09/14/2023] [Indexed: 10/21/2023]
Abstract
Infectious diseases continue to pose a significant threat to the health of humans globally. While the spread of pathogens transcends geographical boundaries, the management of infectious diseases typically occurs within distinct spatial units, determined by geopolitical boundaries. The allocation of management resources within and across regions (the "governance structure") can affect epidemiological outcomes considerably, and policy-makers are often confronted with a choice between applying control measures uniformly or differentially across regions. Here, we investigate the extent to which uniform and non-uniform governance structures affect the costs of an infectious disease outbreak in two-patch systems using an optimal control framework. A uniform policy implements control measures with the same time varying rate functions across both patches, while these measures are allowed to differ between the patches in a non-uniform policy. We compare results from two systems of differential equations representing transmission of cholera and Ebola, respectively, to understand the interplay between transmission mode, governance structure and the optimal control of outbreaks. In our case studies, the governance structure has a meaningful impact on the allocation of resources and burden of cases, although the difference in total costs is minimal. Understanding how governance structure affects both the optimal control functions and epidemiological outcomes is crucial for the effective management of infectious diseases going forward.
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Affiliation(s)
- Emily Howerton
- Department of Biology and Center for Infectious Disease Dynamics, Pennsylvania State University, University Park, PA, USA
| | - Kyle Dahlin
- Center for the Ecology of Infectious Diseases, Odum School of Ecology, University of Georgia, Athens, GA, USA.
| | | | - Lindsey Fox
- Mathematics Discipline, Eckerd College, Saint Petersburg, FL, USA
| | - Margaret Reynolds
- Department of Mathematical Sciences, United States Military Academy, West Point, NY, USA
| | | | - George Lytle
- Department of Biology, Chemistry, Mathematics, and Computer Science, University of Montevallo, Montevallo, AL, USA
| | - Melody Walker
- Department of Medicine, University of Florida, Gainesville, FL, USA
| | - Julie Blackwood
- Department of Mathematics and Statistics, Williams College, Williamstown, MA, USA
| | - Suzanne Lenhart
- Department of Mathematics, University of Tennessee, Knoxville, TN, USA
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6
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Yang J, Jia P, Wang J, Jin Z. Rich dynamics of a bidirectionally linked immuno-epidemiological model for cholera. J Math Biol 2023; 87:71. [PMID: 37848667 DOI: 10.1007/s00285-023-02009-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Revised: 09/24/2023] [Accepted: 10/03/2023] [Indexed: 10/19/2023]
Abstract
Cholera is an environmentally driven disease where the human hosts both ingest the pathogen from polluted environment and shed the pathogen to the environment, generating a two-way feedback cycle. In this paper, we propose a bidirectionally linked immuno-epidemiological model to study the interaction of within- and between-host cholera dynamics. We conduct a rigorous analysis for this multiscale model, with a focus on the stability and bifurcation properties of each feasible equilibrium. We find that the parameter that represents the bidirectional connection is a key factor in shaping the rich dynamics of the system, including the occurrence of the backward bifurcation and Hopf bifurcation. Numerical results illustrate a practical application of our model and add new insight into the prevention and intervention of cholera epidemics.
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Affiliation(s)
- Junyuan Yang
- Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, People's Republic of China.
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, 030006, People's Republic of China.
| | - Peiqi Jia
- Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, People's Republic of China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, 030006, People's Republic of China
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, People's Republic of China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, 030006, People's Republic of China
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7
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Musundi B. An immuno-epidemiological model linking between-host and within-host dynamics of cholera. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:16015-16032. [PMID: 37920000 DOI: 10.3934/mbe.2023714] [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] [Indexed: 11/04/2023]
Abstract
Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health, with a yearly estimated global burden of 2.9 million cases. Although most existing models for the disease focus on its population dynamics, the disease evolves from within-host processes to the population, making it imperative to link the multiple scales of the disease to gain better perspectives on its spread and control. In this study, we propose an immuno-epidemiological model that links the between-host and within-host dynamics of cholera. The immunological (within-host) model depicts the interaction of the cholera pathogen with the adaptive immune response. We distinguish pathogen dynamics from immune response dynamics by assigning different time scales. Through a time-scale analysis, we characterise a single infected person by their immune response. Contrary to other within-host models, this modelling approach allows for recovery through pathogen clearance after a finite time. Then, we scale up the dynamics of the infected person to construct an epidemic model, where the infected population is structured by individual immunological dynamics. We derive the basic reproduction number ($ \mathcal{R}_0 $) and analyse the stability of the equilibrium points. At the disease-free equilibrium, the disease will either be eradicated if $ \mathcal{R}_0 < 1 $ or otherwise persists. A unique endemic equilibrium exists when $ \mathcal{R}_0 > 1 $ and is locally asymptotically stable without a loss of immunity.
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Affiliation(s)
- Beryl Musundi
- Faculty of Mathematics, Technische Universität München, 85748 Garching, Germany
- Department of Mathematics, Moi University, 3900-30100 Eldoret, Kenya
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8
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Kollepara PK, Chisholm RH, Miller JC. Heterogeneity in network structure switches the dominant transmission mode of infectious diseases. PNAS NEXUS 2023; 2:pgad227. [PMID: 37533729 PMCID: PMC10393287 DOI: 10.1093/pnasnexus/pgad227] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 06/20/2023] [Accepted: 06/29/2023] [Indexed: 08/04/2023]
Abstract
Several recent emerging diseases have exhibited both sexual and nonsexual transmission modes (Ebola, Zika, and mpox). In the recent mpox outbreaks, transmission through sexual contacts appears to be the dominant mode of transmission. Motivated by this, we use an SIR-like model to argue that an initially dominant sexual transmission mode can be overtaken by casual transmission at later stages, even if the basic casual reproduction number is less than one. Our results highlight the risk of intervention designs which are informed only by the early dynamics of the disease.
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Affiliation(s)
- Pratyush K Kollepara
- Department of Mathematical and Physical Sciences, La Trobe University, Plenty Rd and Kingsbury Dr, Melbourne, 3086 VIC, Australia
| | - Rebecca H Chisholm
- Department of Mathematical and Physical Sciences, La Trobe University, Plenty Rd and Kingsbury Dr, Melbourne, 3086 VIC, Australia
- Melbourne School of Population and Global Health, The University of Melbourne, Grattan St, Melbourne, 3010 VIC, Australia
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9
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Yang C, Wang J. Computation of the basic reproduction numbers for reaction-diffusion epidemic models. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:15201-15218. [PMID: 37679177 PMCID: PMC10491886 DOI: 10.3934/mbe.2023680] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/09/2023]
Abstract
We consider a class of $ k $-dimensional reaction-diffusion epidemic models ($ k = 1, 2, \cdots $) that are developed from autonomous ODE systems. We present a computational approach for the calculation and analysis of their basic reproduction numbers. Particularly, we apply matrix theory to study the relationship between the basic reproduction numbers of the PDE models and those of their underlying ODE models. We show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important scenarios. We additionally provide two numerical examples to verify our analytical results.
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Affiliation(s)
- Chayu Yang
- Department of Mathematics, University of Nebraska-Lincoln, 1400 R Street, Lincoln, NE 68588, USA
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403, USA
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10
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Choi D, Lee Y, Lin ZH, Cho S, Kim M, Ao CK, Soh S, Sohn C, Jeong CK, Lee J, Lee M, Lee S, Ryu J, Parashar P, Cho Y, Ahn J, Kim ID, Jiang F, Lee PS, Khandelwal G, Kim SJ, Kim HS, Song HC, Kim M, Nah J, Kim W, Menge HG, Park YT, Xu W, Hao J, Park H, Lee JH, Lee DM, Kim SW, Park JY, Zhang H, Zi Y, Guo R, Cheng J, Yang Z, Xie Y, Lee S, Chung J, Oh IK, Kim JS, Cheng T, Gao Q, Cheng G, Gu G, Shim M, Jung J, Yun C, Zhang C, Liu G, Chen Y, Kim S, Chen X, Hu J, Pu X, Guo ZH, Wang X, Chen J, Xiao X, Xie X, Jarin M, Zhang H, Lai YC, He T, Kim H, Park I, Ahn J, Huynh ND, Yang Y, Wang ZL, Baik JM, Choi D. Recent Advances in Triboelectric Nanogenerators: From Technological Progress to Commercial Applications. ACS NANO 2023; 17:11087-11219. [PMID: 37219021 PMCID: PMC10312207 DOI: 10.1021/acsnano.2c12458] [Citation(s) in RCA: 43] [Impact Index Per Article: 43.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 04/20/2023] [Indexed: 05/24/2023]
Abstract
Serious climate changes and energy-related environmental problems are currently critical issues in the world. In order to reduce carbon emissions and save our environment, renewable energy harvesting technologies will serve as a key solution in the near future. Among them, triboelectric nanogenerators (TENGs), which is one of the most promising mechanical energy harvesters by means of contact electrification phenomenon, are explosively developing due to abundant wasting mechanical energy sources and a number of superior advantages in a wide availability and selection of materials, relatively simple device configurations, and low-cost processing. Significant experimental and theoretical efforts have been achieved toward understanding fundamental behaviors and a wide range of demonstrations since its report in 2012. As a result, considerable technological advancement has been exhibited and it advances the timeline of achievement in the proposed roadmap. Now, the technology has reached the stage of prototype development with verification of performance beyond the lab scale environment toward its commercialization. In this review, distinguished authors in the world worked together to summarize the state of the art in theory, materials, devices, systems, circuits, and applications in TENG fields. The great research achievements of researchers in this field around the world over the past decade are expected to play a major role in coming to fruition of unexpectedly accelerated technological advances over the next decade.
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Affiliation(s)
- Dongwhi Choi
- Department
of Mechanical Engineering (Integrated Engineering Program), Kyung Hee University, Yongin, Gyeonggi 17104, South Korea
| | - Younghoon Lee
- Department
of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
- Department
of Mechanical Engineering, Soft Robotics Research Center, Seoul National University, Seoul 08826, South Korea
- Department
of Mechanical Engineering, Gachon University, Seongnam 13120, Korea
| | - Zong-Hong Lin
- Department
of Mechanical Engineering (Integrated Engineering Program), Kyung Hee University, Yongin, Gyeonggi 17104, South Korea
- Department
of Biomedical Engineering, National Taiwan
University, Taipei 10617, Taiwan
- Frontier
Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Sumin Cho
- Department
of Mechanical Engineering (Integrated Engineering Program), Kyung Hee University, Yongin, Gyeonggi 17104, South Korea
| | - Miso Kim
- School
of Advanced Materials Science & Engineering, Sungkyunkwan University, Suwon 16419, Republic
of Korea
- SKKU
Institute of Energy Science and Technology (SIEST), Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
| | - Chi Kit Ao
- Department
of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, 117585, Singapore
| | - Siowling Soh
- Department
of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, 117585, Singapore
| | - Changwan Sohn
- Division
of Advanced Materials Engineering, Jeonbuk
National University, 567 Baekje-daero, Deokjin-gu, Jeonju, Jeonbuk 54896, South Korea
- Department
of Energy Storage/Conversion Engineering of Graduate School (BK21
FOUR), Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju, Jeonbuk 54896, South Korea
| | - Chang Kyu Jeong
- Division
of Advanced Materials Engineering, Jeonbuk
National University, 567 Baekje-daero, Deokjin-gu, Jeonju, Jeonbuk 54896, South Korea
- Department
of Energy Storage/Conversion Engineering of Graduate School (BK21
FOUR), Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju, Jeonbuk 54896, South Korea
| | - Jeongwan Lee
- Department
of Physics, Inha University, 100 Inha-ro, Michuhol-gu, Incheon 22212, South Korea
| | - Minbaek Lee
- Department
of Physics, Inha University, 100 Inha-ro, Michuhol-gu, Incheon 22212, South Korea
| | - Seungah Lee
- School
of Materials Science & Engineering, Yeungnam University, Gyeongsan, Gyeongbuk 38541, South Korea
| | - Jungho Ryu
- School
of Materials Science & Engineering, Yeungnam University, Gyeongsan, Gyeongbuk 38541, South Korea
| | - Parag Parashar
- Department
of Biomedical Engineering, National Taiwan
University, Taipei 10617, Taiwan
| | - Yujang Cho
- Department
of Materials Science and Engineering, Korea
Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro,
Yuseong-gu, Daejeon 34141, Republic of Korea
| | - Jaewan Ahn
- Department
of Materials Science and Engineering, Korea
Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro,
Yuseong-gu, Daejeon 34141, Republic of Korea
| | - Il-Doo Kim
- Department
of Materials Science and Engineering, Korea
Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro,
Yuseong-gu, Daejeon 34141, Republic of Korea
| | - Feng Jiang
- School
of Materials Science and Engineering, Nanyang
Technological University, 50 Nanyang Avenue, 639798, Singapore
- Institute of Flexible
Electronics Technology of Tsinghua, Jiaxing, Zhejiang 314000, China
| | - Pooi See Lee
- School
of Materials Science and Engineering, Nanyang
Technological University, 50 Nanyang Avenue, 639798, Singapore
| | - Gaurav Khandelwal
- Nanomaterials
and System Lab, Major of Mechatronics Engineering, Faculty of Applied
Energy System, Jeju National University, Jeju 632-43, South Korea
- School
of Engineering, University of Glasgow, Glasgow G128QQ, U. K.
| | - Sang-Jae Kim
- Nanomaterials
and System Lab, Major of Mechatronics Engineering, Faculty of Applied
Energy System, Jeju National University, Jeju 632-43, South Korea
| | - Hyun Soo Kim
- Electronic
Materials Research Center, Korea Institute
of Science and Technology (KIST), Seoul 02792, Republic of Korea
- Department
of Physics, Inha University, Incheon 22212, Republic of Korea
| | - Hyun-Cheol Song
- Electronic
Materials Research Center, Korea Institute
of Science and Technology (KIST), Seoul 02792, Republic of Korea
- KIST-SKKU
Carbon-Neutral Research Center, Sungkyunkwan
University (SKKU), Suwon 16419, Republic
of Korea
| | - Minje Kim
- Department
of Electrical Engineering, College of Engineering, Chungnam National University, 34134, Daehak-ro, Yuseong-gu, Daejeon 34134, South Korea
| | - Junghyo Nah
- Department
of Electrical Engineering, College of Engineering, Chungnam National University, 34134, Daehak-ro, Yuseong-gu, Daejeon 34134, South Korea
| | - Wook Kim
- School
of Mechanical Engineering, College of Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
| | - Habtamu Gebeyehu Menge
- Department
of Mechanical Engineering, College of Engineering, Myongji University, 116 Myongji-ro, Cheoin-gu, Yongin, Gyeonggi 17058, Republic of Korea
| | - Yong Tae Park
- Department
of Mechanical Engineering, College of Engineering, Myongji University, 116 Myongji-ro, Cheoin-gu, Yongin, Gyeonggi 17058, Republic of Korea
| | - Wei Xu
- Research
Centre for Humanoid Sensing, Zhejiang Lab, Hangzhou 311100, P. R. China
| | - Jianhua Hao
- Department
of Applied Physics, The Hong Kong Polytechnic
University, Hong Kong, P.R. China
| | - Hyosik Park
- Department
of Energy Science and Engineering, Daegu
Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea
| | - Ju-Hyuck Lee
- Department
of Energy Science and Engineering, Daegu
Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea
| | - Dong-Min Lee
- School
of Advanced Materials Science & Engineering, Sungkyunkwan University, Suwon 16419, Republic
of Korea
| | - Sang-Woo Kim
- School
of Advanced Materials Science & Engineering, Sungkyunkwan University, Suwon 16419, Republic
of Korea
- SKKU
Institute of Energy Science and Technology (SIEST), Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
- Samsung
Advanced Institute for Health Sciences & Technology (SAIHST), Sungkyunkwan University, 115, Irwon-ro, Gangnam-gu, Seoul 06351, South Korea
- SKKU
Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
| | - Ji Young Park
- School
of Advanced Materials Science & Engineering, Sungkyunkwan University, Suwon 16419, Republic
of Korea
| | - Haixia Zhang
- National
Key Laboratory of Science and Technology on Micro/Nano Fabrication;
Beijing Advanced Innovation Center for Integrated Circuits, School
of Integrated Circuits, Peking University, Beijing 100871, China
| | - Yunlong Zi
- Thrust
of Sustainable Energy and Environment, The
Hong Kong University of Science and Technology (Guangzhou), Nansha, Guangdong 511400, China
| | - Ru Guo
- Thrust
of Sustainable Energy and Environment, The
Hong Kong University of Science and Technology (Guangzhou), Nansha, Guangdong 511400, China
| | - Jia Cheng
- State
Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical
Engineering, Tsinghua University, Beijing 100084, China
| | - Ze Yang
- State
Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical
Engineering, Tsinghua University, Beijing 100084, China
| | - Yannan Xie
- College
of Automation & Artificial Intelligence, State Key Laboratory
of Organic Electronics and Information Displays & Institute of
Advanced Materials, Jiangsu Key Laboratory for Biosensors, Jiangsu
National Synergetic Innovation Center for Advanced Materials, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, China
| | - Sangmin Lee
- School
of Mechanical Engineering, Chung-ang University, 84, Heukseok-ro, Dongjak-gu, Seoul 06974, South Korea
| | - Jihoon Chung
- Department
of Mechanical Design Engineering, Kumoh
National Institute of Technology (KIT), 61 Daehak-ro, Gumi, Gyeongbuk 39177, South Korea
| | - Il-Kwon Oh
- National
Creative Research Initiative for Functionally Antagonistic Nano-Engineering,
Department of Mechanical Engineering, School of Mechanical and Aerospace
Engineering, Korea Advanced Institute of
Science and Technology (KAIST), Daejeon 34141, South Korea
| | - Ji-Seok Kim
- National
Creative Research Initiative for Functionally Antagonistic Nano-Engineering,
Department of Mechanical Engineering, School of Mechanical and Aerospace
Engineering, Korea Advanced Institute of
Science and Technology (KAIST), Daejeon 34141, South Korea
| | - Tinghai Cheng
- Beijing
Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, China
| | - Qi Gao
- Beijing
Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, China
| | - Gang Cheng
- Key
Lab for Special Functional Materials, Ministry of Education, National
& Local Joint Engineering Research Center for High-efficiency
Display and Lighting Technology, School of Materials Science and Engineering,
and Collaborative Innovation Center of Nano Functional Materials and
Applications, Henan University, Kaifeng 475004, China
| | - Guangqin Gu
- Key
Lab for Special Functional Materials, Ministry of Education, National
& Local Joint Engineering Research Center for High-efficiency
Display and Lighting Technology, School of Materials Science and Engineering,
and Collaborative Innovation Center of Nano Functional Materials and
Applications, Henan University, Kaifeng 475004, China
| | - Minseob Shim
- Department
of Electronic Engineering, College of Engineering, Gyeongsang National University, 501, Jinjudae-ro, Gaho-dong, Jinju 52828, South Korea
| | - Jeehoon Jung
- Department
of Electrical Engineering, College of Information and Biotechnology, Ulsan National Institute of Science and Technology
(UNIST), 50, UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 44919, South Korea
| | - Changwoo Yun
- Department
of Electrical Engineering, College of Information and Biotechnology, Ulsan National Institute of Science and Technology
(UNIST), 50, UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 44919, South Korea
| | - Chi Zhang
- CAS
Center for Excellence in Nanoscience, Beijing Key Laboratory of Micro-nano
Energy and Sensor, Beijing Institute of
Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, China
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
| | - Guoxu Liu
- CAS
Center for Excellence in Nanoscience, Beijing Key Laboratory of Micro-nano
Energy and Sensor, Beijing Institute of
Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, China
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
| | - Yufeng Chen
- Department
of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Suhan Kim
- Department
of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Xiangyu Chen
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
- CAS
Center for Excellence in Nanoscience, Beijing
Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, 100083 Beijing, China
| | - Jun Hu
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
- CAS
Center for Excellence in Nanoscience, Beijing
Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, 100083 Beijing, China
| | - Xiong Pu
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
- CAS
Center for Excellence in Nanoscience, Beijing
Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, 100083 Beijing, China
| | - Zi Hao Guo
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
- CAS
Center for Excellence in Nanoscience, Beijing
Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, 100083 Beijing, China
| | - Xudong Wang
- Department
of Materials Science and Engineering, University
of Wisconsin−Madison, Madison, Wisconsin 53706, United States
| | - Jun Chen
- Department
of Bioengineering, University of California,
Los Angeles, Los Angeles, California 90095, United States
| | - Xiao Xiao
- Department
of Bioengineering, University of California,
Los Angeles, Los Angeles, California 90095, United States
| | - Xing Xie
- School
of Civil & Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Mourin Jarin
- School
of Civil & Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Hulin Zhang
- College
of Information and Computer, Taiyuan University
of Technology, Taiyuan 030024, P. R. China
| | - Ying-Chih Lai
- Department
of Materials Science and Engineering, National
Chung Hsing University, Taichung 40227, Taiwan
- i-Center
for Advanced Science and Technology, National
Chung Hsing University, Taichung 40227, Taiwan
- Innovation
and Development Center of Sustainable Agriculture, National Chung Hsing University, Taichung 40227, Taiwan
| | - Tianyiyi He
- Department
of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576, Singapore
| | - Hakjeong Kim
- School
of Mechanical Engineering, College of Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
| | - Inkyu Park
- Department
of Mechanical Engineering, Korea Advanced
Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea
| | - Junseong Ahn
- Department
of Mechanical Engineering, Korea Advanced
Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea
| | - Nghia Dinh Huynh
- School
of Mechanical Engineering, College of Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
| | - Ya Yang
- CAS
Center for Excellence in Nanoscience, Beijing Key Laboratory of Micro-nano
Energy and Sensor, Beijing Institute of
Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, China
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
- Center
on Nanoenergy Research, School of Physical Science and Technology, Guangxi University, Nanning 530004, P. R. China
| | - Zhong Lin Wang
- Beijing
Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, China
- School
of Nanoscience and Technology, University
of Chinese Academy of Sciences, Beijing 100049, China
- School
of Materials Science and Engineering, Georgia
Institute of Technology, Atlanta, Georgia 30332, United States
| | - Jeong Min Baik
- School
of Advanced Materials Science & Engineering, Sungkyunkwan University, Suwon 16419, Republic
of Korea
- SKKU
Institute of Energy Science and Technology (SIEST), Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
- KIST-SKKU
Carbon-Neutral Research Center, Sungkyunkwan
University (SKKU), Suwon 16419, Republic
of Korea
| | - Dukhyun Choi
- SKKU
Institute of Energy Science and Technology (SIEST), Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
- School
of Mechanical Engineering, College of Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi 16419, South Korea
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11
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Gentry Z, Zhao L, Faust RA, David RE, Norton J, Xagoraraki I. Wastewater surveillance beyond COVID-19: a ranking system for communicable disease testing in the tri-county Detroit area, Michigan, USA. Front Public Health 2023; 11:1178515. [PMID: 37333521 PMCID: PMC10272568 DOI: 10.3389/fpubh.2023.1178515] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 05/12/2023] [Indexed: 06/20/2023] Open
Abstract
Introduction Throughout the coronavirus disease 2019 (COVID-19) pandemic, wastewater surveillance has been utilized to monitor the disease in the United States through routine national, statewide, and regional monitoring projects. A significant canon of evidence was produced showing that wastewater surveillance is a credible and effective tool for disease monitoring. Hence, the application of wastewater surveillance can extend beyond monitoring SARS-CoV-2 to encompass a diverse range of emerging diseases. This article proposed a ranking system for prioritizing reportable communicable diseases (CDs) in the Tri-County Detroit Area (TCDA), Michigan, for future wastewater surveillance applications at the Great Lakes Water Authority's Water Reclamation Plant (GLWA's WRP). Methods The comprehensive CD wastewater surveillance ranking system (CDWSRank) was developed based on 6 binary and 6 quantitative parameters. The final ranking scores of CDs were computed by summing the multiplication products of weighting factors for each parameter, and then were sorted based on decreasing priority. Disease incidence data from 2014 to 2021 were collected for the TCDA. Disease incidence trends in the TCDA were endowed with higher weights, prioritizing the TCDA over the state of Michigan. Results Disparities in incidences of CDs were identified between the TCDA and state of Michigan, indicating epidemiological differences. Among 96 ranked CDs, some top ranked CDs did not present relatively high incidences but were prioritized, suggesting that such CDs require significant attention by wastewater surveillance practitioners, despite their relatively low incidences in the geographic area of interest. Appropriate wastewater sample concentration methods are summarized for the application of wastewater surveillance as per viral, bacterial, parasitic, and fungal pathogens. Discussion The CDWSRank system is one of the first of its kind to provide an empirical approach to prioritize CDs for wastewater surveillance, specifically in geographies served by centralized wastewater collection in the area of interest. The CDWSRank system provides a methodological tool and critical information that can help public health officials and policymakers allocate resources. It can be used to prioritize disease surveillance efforts and ensure that public health interventions are targeted at the most potentially urgent threats. The CDWSRank system can be easily adopted to geographical locations beyond the TCDA.
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Affiliation(s)
- Zachary Gentry
- Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, United States
| | - Liang Zhao
- Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, United States
| | | | - Randy E. David
- Wayne State University School of Medicine, Detroit, MI, United States
| | - John Norton
- Great Lakes Water Authority, Detroit, MI, United States
| | - Irene Xagoraraki
- Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, United States
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12
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Li KL, Yang JY, Li XZ. Analysis of an environmental epidemic model based on voluntary vaccination policy. Comput Methods Biomech Biomed Engin 2023; 26:595-611. [PMID: 35608391 DOI: 10.1080/10255842.2022.2079080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
With the worsening of the environment and the increasing international trade, indirect transmission from exposure to contaminants in the surrounding environment has become an overlooked mode of transmission. This paper proposes a new game-theoretic model considering voluntary vaccination against imperfection and the unique integration of human-to-human and virus-to-human transmission routes. Based on the individual-based risk assessment update rule (IB-RA), the strategy-based risk assessment update rule (SB-RA), and the direct commitment update rule (DC), the different effects of individuals' behaviors on disease prevalence are analyzed. To find the effect of indirect transmission on epidemic transmission, we compare our model with the traditional SVIR model. Finally, it can be seen that indirect transmission mechanisms will aggravate the spread of epidemics.
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Affiliation(s)
- Ke-Lu Li
- School of Mathematics and Information Science, Henan Normal University, Xinxiang, China
| | - Jun-Yuan Yang
- Complex Systems Research Center, Shanxi University, Taiyuan, China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, China
| | - Xue-Zhi Li
- School of Mathematics and Information Science, Henan Normal University, Xinxiang, China
- School of Statistics and Mathematics, Henan Finance University, Zhengzhou, China
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13
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Igoe M, Casagrandi R, Gatto M, Hoover CM, Mari L, Ngonghala CN, Remais JV, Sanchirico JN, Sokolow SH, Lenhart S, de Leo G. Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries. Bull Math Biol 2023; 85:31. [PMID: 36907932 PMCID: PMC10008208 DOI: 10.1007/s11538-023-01137-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 02/20/2023] [Indexed: 03/14/2023]
Abstract
Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.
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Affiliation(s)
- Morganne Igoe
- Department of Mathematics, University of Tennessee, Knoxville, TN, USA.
| | - Renato Casagrandi
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | - Marino Gatto
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | - Christopher M Hoover
- Division of Environmental Health Sciences, University of California, Berkeley, Berkeley, CA, USA
| | - Lorenzo Mari
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | | | - Justin V Remais
- Division of Environmental Health Sciences, University of California, Berkeley, Berkeley, CA, USA
| | - James N Sanchirico
- Environmental Science and Policy, University of California, Davis, Davis, CA, USA
| | - Susanne H Sokolow
- Stanford Program for Diseases Ecology, Health and the Environment, Stanford University, Pacific Grove, CA, USA
| | - Suzanne Lenhart
- Department of Mathematics, University of Tennessee, Knoxville, TN, USA
| | - Giulio de Leo
- Department of Earth System Science and Department of Oceans, Hopkins Marine Station, Stanford Doerr School of Sustainability, Stanford University, Pacific Grove, CA, USA
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14
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Li W, Zhang Y, Ji J, Huang L. Dynamics of a diffusion epidemic SIRI system in heterogeneous environment. ZEITSCHRIFT FUER ANGEWANDTE MATHEMATIK UND PHYSIK 2023; 74:104. [PMID: 37153518 PMCID: PMC10140731 DOI: 10.1007/s00033-023-02002-z] [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: 11/07/2021] [Revised: 12/04/2022] [Accepted: 04/14/2023] [Indexed: 05/09/2023]
Abstract
This paper studies the dynamical behaviors of a diffusion epidemic SIRI system with distinct dispersal rates. The overall solution of the system is derived by using L p theory and the Young's inequality. The uniformly boundedness of the solution is obtained for the system. The asymptotic smoothness of the semi-flow and the existence of the global attractor are discussed. Moreover, the basic reproduction number is defined in a spatially uniform environment and the threshold dynamical behaviors are obtained for extinction or continuous persistence of disease. When the spread rate of the susceptible individuals or the infected individuals is close to zero, the asymptotic profiles of the system are studied. This can help us to better understand the dynamic characteristics of the model in a bounded space domain with zero flux boundary conditions.
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Affiliation(s)
- Wenjie Li
- Department of Systems and Applied Mathematics, Kunming University of Science and Technology, Kunming, 650500 Yunnan People’s Republic of China
| | - Ying Zhang
- Department of Systems and Applied Mathematics, Kunming University of Science and Technology, Kunming, 650500 Yunnan People’s Republic of China
| | - Jinchen Ji
- School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Broadway, NSW 2007 Australia
| | - Lihong Huang
- College of Mathematics and Computer Science, Changsha University, Changsha, 410022 Hunan People’s Republic of China
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15
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Cui X, Xue D, Pan F. A fractional SVIR-B epidemic model for Cholera with imperfect vaccination and saturated treatment. EUROPEAN PHYSICAL JOURNAL PLUS 2022; 137:1361. [PMID: 36569382 PMCID: PMC9768410 DOI: 10.1140/epjp/s13360-022-03564-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Accepted: 11/25/2022] [Indexed: 06/17/2023]
Abstract
Given the limited medical resources in most cholera endemic countries, in this paper, a nonlinear fractional SVIR-B (Susceptible-Vaccinated-Infected-Recovered, Bacterial) cholera epidemic model with imperfect vaccination and saturated treatment is proposed and investigated. The model performs well-posed in both epidemiologically and mathematically, especially, we demonstrate the positivity and boundedness of all solutions using the generalized mean value theorem. The control reproduction number R vt is derived using the next generation matrix method and both local and global stability analyses for the disease-free equilibrium is performed by analyzing the characteristic equation and using Lyapunov functional. Then, the existence and stability of endemic equilibria are further addressed. Sufficient conditions for the existence of backward bifurcation and Hopf bifurcation are also derived. Subsequently, an optimal control problem with vaccination, media coverage, treatment, and sanitation as control strategies is proposed and analyzed, providing a rationale for cholera control and prevention. In addition, several numerical examples are employed to illustrate our theoretical results.
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Affiliation(s)
- Xinshu Cui
- College of Information Science and Engineering, Northeastern University, Shenyang, 110819 People’s Republic of China
| | - Dingyu Xue
- College of Information Science and Engineering, Northeastern University, Shenyang, 110819 People’s Republic of China
| | - Feng Pan
- College of Information Science and Engineering, Northeastern University, Shenyang, 110819 People’s Republic of China
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16
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Brouwer AF, Eisenberg MC, Bakker KM, Boerger SN, Zahid MH, Freeman MC, Eisenberg JNS. Leveraging infectious disease models to interpret randomized controlled trials: Controlling enteric pathogen transmission through water, sanitation, and hygiene interventions. PLoS Comput Biol 2022; 18:e1010748. [DOI: 10.1371/journal.pcbi.1010748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 12/15/2022] [Accepted: 11/18/2022] [Indexed: 12/12/2022] Open
Abstract
Randomized controlled trials (RCTs) evaluate hypotheses in specific contexts and are often considered the gold standard of evidence for infectious disease interventions, but their results cannot immediately generalize to other contexts (e.g., different populations, interventions, or disease burdens). Mechanistic models are one approach to generalizing findings between contexts, but infectious disease transmission models (IDTMs) are not immediately suited for analyzing RCTs, since they often rely on time-series surveillance data. We developed an IDTM framework to explain relative risk outcomes of an infectious disease RCT and applied it to a water, sanitation, and hygiene (WASH) RCT. This model can generalize the RCT results to other contexts and conditions. We developed this compartmental IDTM framework to account for key WASH RCT factors: i) transmission across multiple environmental pathways, ii) multiple interventions applied individually and in combination, iii) adherence to interventions or preexisting conditions, and iv) the impact of individuals not enrolled in the study. We employed a hybrid sampling and estimation framework to obtain posterior estimates of mechanistic parameter sets consistent with empirical outcomes. We illustrated our model using WASH Benefits Bangladesh RCT data (n = 17,187). Our model reproduced reported diarrheal prevalence in this RCT. The baseline estimate of the basic reproduction number R 0 for the control arm (1.10, 95% CrI: 1.07, 1.16) corresponded to an endemic prevalence of 9.5% (95% CrI: 7.4, 13.7%) in the absence of interventions or preexisting WASH conditions. No single pathway was likely able to sustain transmission: pathway-specific R 0 s for water, fomites, and all other pathways were 0.42 (95% CrI: 0.03, 0.97), 0.20 (95% CrI: 0.02, 0.59), and 0.48 (95% CrI: 0.02, 0.94), respectively. An IDTM approach to evaluating RCTs can complement RCT analysis by providing a rigorous framework for generating data-driven hypotheses that explain trial findings, particularly unexpected null results, opening up existing data to deeper epidemiological understanding.
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17
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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: 7] [Impact Index Per Article: 3.5] [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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18
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Collins O, Duffy K. A mathematical model for the dynamics and control of malaria in Nigeria. Infect Dis Model 2022; 7:728-741. [DOI: 10.1016/j.idm.2022.10.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Revised: 10/19/2022] [Accepted: 10/25/2022] [Indexed: 11/06/2022] Open
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19
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Saucedo O, Tien JH. Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networks. Infect Dis Model 2022; 7:742-760. [DOI: 10.1016/j.idm.2022.10.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 09/04/2022] [Accepted: 10/26/2022] [Indexed: 11/06/2022] Open
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20
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Singh A, Deolia P. COVID-19 outbreak: a predictive mathematical study incorporating shedding effect. JOURNAL OF APPLIED MATHEMATICS & COMPUTING 2022; 69:1239-1268. [PMID: 36158635 PMCID: PMC9484852 DOI: 10.1007/s12190-022-01792-1] [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: 02/07/2022] [Revised: 08/27/2022] [Accepted: 09/11/2022] [Indexed: 06/16/2023]
Abstract
In this paper, a modified SEIR epidemic model incorporating shedding effect is proposed to analyze transmission dynamics of the COVID-19 virus among different individuals' classes. The direct impact of pathogen concentration over susceptible populations through the shedding of COVID-19 virus into the environment is investigated. Moreover, the threshold value of shedding parameters is computed which gives information about their significance in decreasing the impact of the disease. The basic reproduction number ( R 0 ) is calculated using the next-generation matrix method, taking shedding as a new infection. In the absence of disease, the condition for the equilibrium point to be locally and globally asymptotically stable with R 0 < 1 are established. It has been shown that the unique endemic equilibrium point is globally asymptotically stable under the condition R 0 > 1 . Bifurcation theory and center manifold theorem imply that the system exhibit backward bifurcation at R 0 = 1 . The sensitivity indices of R 0 are computed to investigate the robustness of model parameters. The numerical simulation is demonstrated to illustrate the results.
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Affiliation(s)
- Anuraj Singh
- ABV-Indian Institute of Information Technology and Management, Gwalior, M.P. India
| | - Preeti Deolia
- ABV-Indian Institute of Information Technology and Management, Gwalior, M.P. India
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21
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Liu Z, Jin Z, Yang J, Zhang J. The backward bifurcation of an age-structured cholera transmission model with saturation incidence. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:12427-12447. [PMID: 36654005 DOI: 10.3934/mbe.2022580] [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
In this paper, we consider an age-structured cholera model with saturation incidence, vaccination age of vaccinated individuals, infection age of infected individuals, and biological age of pathogens. First, the basic reproduction number is calculated. When the basic reproduction number is less than one, the disease-free equilibrium is locally stable. Further, the existence of backward bifurcation of the model is obtained. Numerically, we also compared the effects of various control measures, including basic control measures and vaccination, on the number of infected individuals.
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Affiliation(s)
- Zhiping Liu
- School of Data Science and Technology, North University of China, Taiyuan 030051, Shanxi, China
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China
| | - Junyuan Yang
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China
| | - Juan Zhang
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China
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22
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Getz WM, Salter R, Vissat LL. Simulation applications to support teaching and research in epidemiological dynamics. BMC MEDICAL EDUCATION 2022; 22:632. [PMID: 35987608 PMCID: PMC9391658 DOI: 10.1186/s12909-022-03674-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 07/29/2022] [Indexed: 06/15/2023]
Abstract
BACKGROUND An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP Ⓡ (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs. RESULTS We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that 'burn' through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R0, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R0>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality. CONCLUSION Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.
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Affiliation(s)
- Wayne M Getz
- Department Environmental Science, Policy and Management, University of California, Berkeley, 94720 CA USA
- School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Durban, 4000 South Africa
- Numerus Inc, 850 Iron Point Road, Folsom, 95630 CA USA
| | - Richard Salter
- Numerus Inc, 850 Iron Point Road, Folsom, 95630 CA USA
- Computer Science Department, Oberlin College, Oberlin, 44074 OH USA
| | - Ludovica Luisa Vissat
- Department Environmental Science, Policy and Management, University of California, Berkeley, 94720 CA USA
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Stewart Merrill TE, Cáceres CE, Gray S, Laird VR, Schnitzler ZT, Buck JC. Timescale reverses the relationship between host density and infection risk. Proc Biol Sci 2022; 289:20221106. [PMID: 35919996 PMCID: PMC9346366 DOI: 10.1098/rspb.2022.1106] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 07/08/2022] [Indexed: 12/14/2022] Open
Abstract
Host density shapes infection risk through two opposing phenomena. First, when infective stages are subdivided among multiple hosts, greater host densities decrease infection risk through 'safety in numbers'. Hosts, however, represent resources for parasites, and greater host availability also fuels parasite reproduction. Hence, host density increases infection risk through 'density-dependent transmission'. Theory proposes that these phenomena are not disparate outcomes but occur over different timescales. That is, higher host densities may reduce short-term infection risk, but because they support parasite reproduction, may increase long-term risk. We tested this theory in a zooplankton-disease system with laboratory experiments and field observations. Supporting theory, we found that negative density-risk relationships (safety in numbers) sometimes emerged over short timescales, but these relationships reversed to 'density-dependent transmission' within two generations. By allowing parasite numerical responses to play out, time can shift the consequences of host density, from reduced immediate risk to amplified future risk.
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Affiliation(s)
- Tara E. Stewart Merrill
- Coastal and Marine Laboratory, Florida State University, St. Teresa, FL 32358, USA
- Program in Ecology, Evolution and Conservation Biology, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
| | - Carla E. Cáceres
- Program in Ecology, Evolution and Conservation Biology, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
- School of Integrative Biology, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
| | - Samantha Gray
- School of Integrative Biology, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
| | - Veronika R. Laird
- School of Integrative Biology, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
- Department of Epidemiology, Emory University, Atlanta, GA 30322, USA
| | - Zoe T. Schnitzler
- Program in Ecology, Evolution and Conservation Biology, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
| | - Julia C. Buck
- Biology and Marine Biology, University of North Carolina Wilmington, Wilmington, NC 28403, USA
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Brouwer AF. Why the Spectral Radius? An intuition-building introduction to the basic reproduction number. Bull Math Biol 2022; 84:96. [PMID: 35930076 PMCID: PMC9355935 DOI: 10.1007/s11538-022-01057-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 07/21/2022] [Indexed: 11/26/2022]
Abstract
The basic reproduction number [Formula: see text] is a fundamental concept in mathematical epidemiology and infectious disease modeling. Loosely speaking, it describes the number of people that an infectious person is expected to infect. The basic reproduction number has profound implications for epidemic trajectories and disease control strategies. It is well known that the basic reproduction number can be calculated as the spectral radius of the next generation matrix, but why this is the case may not be intuitively obvious. Here, we walk through how the discrete, next generation process connects to the ordinary differential equation disease system of interest, linearized at the disease-free equilibrium. Then, we use linear algebra to develop a geometric explanation of why the spectral radius of the next generation matrix is an epidemic threshold. Finally, we work through a series of examples that help to build familiarity with the kinds of patterns that arise in parameter combinations produced by the next generation method. This article is intended to help new infectious disease modelers develop intuition for the form and interpretation of the basic reproduction number in their disease systems of interest.
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Affiliation(s)
- Andrew F Brouwer
- Department of Epidemiology, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, 48109, USA.
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Zhao Z, Yang M, Lv J, Hu Q, Chen Q, Lei Z, Wang M, Zhang H, Zhai X, Zhao B, Su Y, Chen Y, Zhang XS, Cui JA, Frutos R, Chen T. Shigellosis seasonality and transmission characteristics in different areas of China: A modelling study. Infect Dis Model 2022; 7:161-178. [PMID: 35662902 PMCID: PMC9144056 DOI: 10.1016/j.idm.2022.05.003] [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: 03/30/2022] [Revised: 05/15/2022] [Accepted: 05/18/2022] [Indexed: 11/30/2022] Open
Abstract
Objective In China, the burden of shigellosis is unevenly distributed, notably across various ages and geographical areas. Shigellosis temporal trends appear to be seasonal. We should clarify seasonal warnings and regional transmission patterns. Method This study adopted a Logistic model to assess the seasonality and a dynamics model to compare the transmission in different areas. The next-generation matrix was used to calculate the effective reproduction number (R eff) to quantify the transmissibility. Results In China, the rate of shigellosis fell from 35.12 cases per 100,000 people in 2005 to 7.85 cases per 100,000 people in 2017, peaking in June and August. After simulation by the Logistic model, the 'peak time' is mainly concentrated from mid-June to mid-July. China's 'early warning time' is primarily focused on from April to May. We predict the 'peak time' of shigellosis is the 6.30th month and the 'early warning time' is 3.87th month in 2021. According to the dynamics model results, the water/food transfer pathway has been mostly blocked off. The transmissibility of different regions varies greatly, such as the mean R eff of Longde County (3.76) is higher than Xiamen City (3.15), higher than Chuxiong City (2.52), and higher than Yichang City (1.70). Conclusion The 'early warning time' for shigellosis in China is from April to May every year, and it may continue to advance in the future, such as the early warning time in 2021 is in mid-March. Furthermore, we should focus on preventing and controlling the person-to-person route of shigellosis and stratified deploy prevention and control measures according to the regional transmission.
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Key Words
- ARIMA, Autoregressive Integrated Moving Average (model)
- CDC, Center of Chinese Center for Disease Control and Prevention
- CI, confidence interval
- Early warning
- MSM, men who sex with a man
- ODE, ordinary differential equation
- R0, basic reproductive number
- R2, Coefficient of determination
- Reff, effective reproduction number
- SD, standard deviation
- SEIAR, Susceptible–Exposed–Infectious/Asymptomatic–Recovered (model)
- SEIARW, Susceptible–Exposed–Infectious/Asymptomatic–Recovered-Water/Food (model)
- Seasonality
- Shigellosis
- Transmissibility
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Affiliation(s)
- Zeyu Zhao
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, People's Republic of China
- CIRAD, UMR 17, Intertryp, Montpellier, France
| | - Meng Yang
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, People's Republic of China
| | - Jinlong Lv
- Department of Mathematics, School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 102616, People's Republic of China
| | - Qingqing Hu
- Division of Public Health, School of Medicine, University of Utah, 201 Presidents Circle, Salt Lake City, 84112, Utah, USA
| | | | - Zhao Lei
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, People's Republic of China
| | - Mingzhai Wang
- Xiamen Center for Disease Control and Prevention, Xiamen City, Fujian Province, People's Republic of China
| | - Hao Zhang
- Yichang Center for Disease Control and Prevention, Yichang City, Hubei Province, People's Republic of China
| | - Xiongjie Zhai
- Longde County Center for Disease Control and Prevention, Guyuan City, Ningxia Hui Autonomous Region, People's Republic of China
| | - Benhua Zhao
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, People's Republic of China
| | - Yanhua Su
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, People's Republic of China
| | - Yong Chen
- Department of Stomatology, School of Medicine, Xiamen University People's Republic of China
| | | | - Jing-An Cui
- Department of Mathematics, School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 102616, People's Republic of China
| | | | - Tianmu Chen
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, People's Republic of China
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Zha X, Tian Y, Xiao J, Yu C. Hydrochemical characteristics of surface waters and their relationships to the Kashin-Beck Disease in Longzi County, Tibet. Sci Rep 2022; 12:7819. [PMID: 35552427 PMCID: PMC9098842 DOI: 10.1038/s41598-022-11463-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Accepted: 04/18/2022] [Indexed: 11/08/2022] Open
Abstract
Although previous studies have been reported between the Kashin-Beck Disease (KBD) epidemic and the hydrochemical characteristics of surface waters, the etiology of the disease remains unclear. In the present study, we comprehensively investigated the relationship between the KBD and the hydrochemical characteristics of surface waters in Longzi County. Results show that, the pH (mean = 7.27 ± 0.30), total hardness (TH, mean = 57.08 ± 45.74 mg L-1), total dissolved solids (TDS, mean = 67.56 ± 44.00 mg L-1) and oxidation-reduction potential (ORP, mean = 84.11 ± 23.55 mV) of surface waters in KBD endemic areas are lower than those in the non-KBD endemic areas (means of pH = 7.49 ± 0.30; TH = 262.06 ± 123.29 mg L-1; TDS = 253.25 ± 100.39 mg L-1; ORP = 215.90 ± 55.99 mV). These results suggest that long-term consumption of low TDS, essential trace elements (e.g., nickel, cobalt, iron, selenium, zinc, molybdenum, and iodine) deficient, and potential toxic elements (e.g., arsenic) enriched waters by humans likely causes the KBD. Environmental factors such as the geology and geomorphology may produce biogeochemical imbalance, geomorphic, vegetation types and local climatic conditions may have significant impact on food fungi toxin poisoning and water organic compound poisoning, and these also impact the KBD occurrence.
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Affiliation(s)
- Xinjie Zha
- Xi'an University of Finance and Economics, Xi'an, 710100, China
| | - Yuan Tian
- Key Laboratory of Ecosystem Network Observation and Modelling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China.
| | - Jianyu Xiao
- Key Laboratory of Ecosystem Network Observation and Modelling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Chengqun Yu
- Key Laboratory of Ecosystem Network Observation and Modelling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China.
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A reaction-advection-diffusion model of cholera epidemics with seasonality and human behavior change. J Math Biol 2022; 84:34. [PMID: 35381862 DOI: 10.1007/s00285-022-01733-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2021] [Revised: 11/19/2021] [Accepted: 03/02/2022] [Indexed: 11/27/2022]
Abstract
Cholera is a water- and food-borne infectious disease caused by V. cholerae. To investigate multiple effects of human behavior change, seasonality and spatial heterogeneity on cholera spread, we propose a reaction-advection-diffusion model that incorporates human hosts and aquatic reservoir of V. cholerae. We derive the basic reproduction number [Formula: see text] for this system and then establish a threshold type result on its global dynamics in terms of [Formula: see text]. Further, we show that the bacterial loss at the downstream end of the river due to water flux can reduce the disease risk, and describe the asymptotic behavior of [Formula: see text] for small and large diffusion in a special case (where the diffusion rates of infected human and the pathogen are constant). We also study the transmission dynamics at the early stage of cholera outbreak numerically, and find that human behavior change may lower the infection level and delay the disease peak. Moreover, the relative rate of bacterial loss, together with convection rate, plays an important role in identifying the severely infected areas. Meanwhile spatial heterogeneity may dilute or amplify cholera infection, which in turn would increase the complexity of disease spread.
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Espira LM, Brouwer AF, Han BA, Foufopoulos J, Eisenberg JNS. Dilution of Epidemic Potential of Environmentally Transmitted Infectious Diseases for Species with Partially Overlapping Habitats. Am Nat 2022; 199:E43-E56. [PMID: 35077275 PMCID: PMC9136953 DOI: 10.1086/717413] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/27/2023]
Abstract
AbstractSpecies diversity may play an important role in the modulation of pathogen transmission through the dilution effect. Infectious disease models can help elucidate mechanisms that may underlie this effect. While many modeling studies have assumed direct host-to-host transmission, many pathogens are transmitted through the environment. We present a mathematical modeling analysis exploring conditions under which we observe the dilution effect in systems with environmental transmission where host species interact through fully or partially overlapping habitats. We measure the strength of the dilution effect by the relative decrease in the basic reproduction number of two-species assemblages compared with that of a focal host species. We find that a dilution effect is most likely when the pathogen is environmentally persistent (frequency-dependent-like transmission). The magnitude of this effect is strongest when the species with the greater epidemic potential is relatively slow to pick up pathogens in the environment (density-dependent transmission) and the species with the lesser epidemic potential is efficient at picking up pathogens (frequency-dependent transmission). These findings suggest that measurable factors, including pathogen persistence and the host's relative efficiency of pathogen pickup, can guide predictions of when biodiversity might lead to a dilution effect and may thus give concrete direction to future ecological work.
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Affiliation(s)
- Leon M. Espira
- Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109
| | - Andrew F. Brouwer
- Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109
| | - Barbara A. Han
- Cary Institute of Ecosystem Studies, Millbrook, NY 12545
| | - Johannes Foufopoulos
- School for Environment and Sustainability, University of Michigan, Ann Arbor, MI 48109
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Cryptocurrency as Epidemiologically Safe Means of Transactions: Diminishing Risk of SARS-CoV-2 Spread. MATHEMATICS 2021. [DOI: 10.3390/math9243263] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
In comparison with other respiratory viruses, the current COVID-19 pandemic’s rapid seizing the world can be attributed to indirect (contact) way of transmission of SARS-CoV-2 virus in addition to the regular airborne way. A significant part of indirect transmission is made through cash bank notes. SARS-CoV-2 remains on cash paper money for period around four times larger than influenza A virus and is absorbed by cash notes two and a half times more effectively than influenza A (our model). During the pandemic, cryptocurrencies have gained attractiveness as an “epidemiologically safe” means of transactions. On the basis of the authors’ gallop polls performed online with social networks users in 44 countries in 2020–2021 (the total number of clear responses after the set repair 32,115), around 14.7% of surveyed participants engaged in cryptocurrency-based transactions during the pandemic. This may be one of the reasons of significant rise of cryptocurrencies rates since mid-March 2020 till the end of 2021. The paper discusses the reasons for cryptocurrency attractiveness during the COVID-19 pandemic. Among them, there are fear of SARS-CoV-2 spread via cash contacts and the ability of the general population to mine cryptocurrencies. The article also provides a breakdown of the polled audience profile to determine the nationalities that have maximal level of trust to saving and transacting money as cryptocurrencies.
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When and why direct transmission models can be used for environmentally persistent pathogens. PLoS Comput Biol 2021; 17:e1009652. [PMID: 34851954 PMCID: PMC8668103 DOI: 10.1371/journal.pcbi.1009652] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Revised: 12/13/2021] [Accepted: 11/16/2021] [Indexed: 01/17/2023] Open
Abstract
Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen’s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models’ mean outputs diverge, with distinct predictions of outbreak size and duration. Mathematical models of the spread and progression of communicable disease in populations are important tools in efforts to prevent and control outbreaks. A common class of disease models assume that infection is transmitted directly from infectious to susceptible individuals when they are in close proximity—so called direct transmission models. These are used widely and have proven invaluable as simplified descriptions of a wide array of infectious diseases in diverse populations. However, many pathogens spread through indirect, environmental routes of transmission, for example via contact with contaminated water sources in the case of cholera, or inhalation of infectious airborne droplets for respiratory infections, such as Covid-19. We show that direct transmission models work well for such pathogens with short environmental lifetimes and where hosts shed pathogens into the environment at high rates. This means that we do not require information about environmental pathogen levels to understand the behaviour of outbreaks caused by these pathogens. When shedding rates are also low, e.g., with macroparasitic infections, or when variable environmental factors play a role in transmissibility, then explicit modelling of both the pathogen and environmental transmission will provide a more accurate picture than a direct transmission approximation.
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Che E, Yakubu AA. A discrete-time risk-structured model of cholera infections in Cameroon. JOURNAL OF BIOLOGICAL DYNAMICS 2021; 15:523-562. [PMID: 34672907 DOI: 10.1080/17513758.2021.1991497] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 05/21/2021] [Indexed: 06/13/2023]
Abstract
In a recent paper, Che et al. [5] used a continuous-time Ordinary Differential Equation (ODE) model with risk structure to study cholera infections in Cameroon. However, the population and the reported cholera cases in Cameroon are censored at discrete-time annual intervals. In this paper, unlike in [5], we introduce a discrete-time risk-structured cholera model with no spatial structure. We use our discrete-time demographic equation to 'fit' the annual population of Cameroon. Furthermore, we use our fitted discrete-time model to capture the annually reported cholera cases from 1987 to 2004 and to study the impact of vaccination, treatment and improved sanitation on the number of cholera infections from 2004 to 2019. Our discrete-time cholera model confirms the results of the ODE model in [5]. However, our discrete-time model predicts a decrease in the number of cholera cases in a shorter period of cholera intervention (2004-2019) as compared to the ODE model's period of intervention (2004-2022).
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Affiliation(s)
- Eric Che
- Department of Mathematics, Howard University, Washington, DC, USA
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32
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Che E, Numfor E, Lenhart S, Yakubu AA. Mathematical modeling of the influence of cultural practices on cholera infections in Cameroon. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:8374-8391. [PMID: 34814304 DOI: 10.3934/mbe.2021415] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The Far North Region of Cameroon, a high risk cholera endemic region, has been experiencing serious and recurrent cholera outbreaks in recent years. Cholera outbreaks in this region are associated with cultural practices (traditional and religious beliefs). In this paper, we introduce a mathematical model of the influence of cultural practices on the dynamics of cholera in the Far North Region. Our model is an SEIR type model with a pathogen class and multiple susceptible classes based on traditional and religious beliefs. Using daily reported cholera cases from three health districts (Kaélé, Kar Hay and Moutourwa) in the Far North Region from June 25, 2019 to August 16, 2019, we estimate parameter values of our model and use Akaike information criterion (AIC) to demonstrate that our model gives a good fit for our data on cholera cases. We use sensitivity analysis to study the impact of each model parameter on the threshold parameter (control reproduction number), Rc, and the number of model predicted cholera cases. Finally, we investigate the effect of cultural practices on the number of cholera cases in the region.
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Affiliation(s)
- Eric Che
- Department of Mathematics, Howard University, Washington, DC 20059, USA
| | - Eric Numfor
- Department of Mathematics, Augusta University, Augusta, GA 30912, USA
| | - Suzanne Lenhart
- Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
| | - Abdul-Aziz Yakubu
- Department of Mathematics, Howard University, Washington, DC 20059, USA
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33
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Shu H, Ma Z, Wang XS. Threshold dynamics of a nonlocal and delayed cholera model in a spatially heterogeneous environment. J Math Biol 2021; 83:41. [PMID: 34559311 DOI: 10.1007/s00285-021-01672-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Revised: 06/19/2021] [Accepted: 09/08/2021] [Indexed: 11/26/2022]
Abstract
A nonlocal and delayed cholera model with two transmission mechanisms in a spatially heterogeneous environment is derived. We introduce two basic reproduction numbers, one is for the bacterium in the environment and the other is for the cholera disease in the host population. If the basic reproduction number for the cholera bacterium in the environment is strictly less than one and the basic reproduction number of infection is no more than one, we prove globally asymptotically stability of the infection-free steady state. Otherwise, the infection will persist and there exists at least one endemic steady state. For the special homogeneous case, the endemic steady state is actually unique and globally asymptotically stable. Under some conditions, the basic reproduction number of infection is strictly decreasing with respect to the diffusion coefficients of cholera bacteria and infectious hosts. When these conditions are violated, numerical simulation suggests that spatial diffusion may not only spread the infection from high-risk region to low-risk region, but also increase the infection level in high-risk region.
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Affiliation(s)
- Hongying Shu
- School of Mathematical Sciences, Tongji University, Shanghai, 200092, China
- School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710062, China
| | - Zongwei Ma
- School of Mathematical Sciences, Tongji University, Shanghai, 200092, China
- College of Data Science, Jiaxing University, Jiaxing, 314001, China
| | - Xiang-Sheng Wang
- Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70503, USA.
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Rosati DP, Woolhouse MH, Bolker BM, Earn DJD. Modelling song popularity as a contagious process. Proc Math Phys Eng Sci 2021; 477:20210457. [PMID: 35153583 PMCID: PMC8455174 DOI: 10.1098/rspa.2021.0457] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Accepted: 08/20/2021] [Indexed: 11/12/2022] Open
Abstract
Popular songs are often said to be 'contagious', 'infectious' or 'viral'. We find that download count time series for many popular songs resemble infectious disease epidemic curves. This paper suggests infectious disease transmission models could help clarify mechanisms that contribute to the 'spread' of song preferences and how these mechanisms underlie song popularity. We analysed data from MixRadio, comprising song downloads through Nokia cell phones in Great Britain from 2007 to 2014. We compared the ability of the standard susceptible-infectious-recovered (SIR) epidemic model and a phenomenological (spline) model to fit download time series of popular songs. We fitted these same models to simulated epidemic time series generated by the SIR model. Song downloads are captured better by the SIR model, to the same extent that actual SIR simulations are fitted better by the SIR model than by splines. This suggests that the social processes underlying song popularity are similar to those that drive infectious disease transmission. We draw conclusions about song popularity within specific genres based on estimated SIR parameters. In particular, we argue that faster spread of preferences for Electronica songs may reflect stronger connectivity of the 'susceptible community', compared with the larger and broader community that listens to more common genres.
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Affiliation(s)
- Dora P. Rosati
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- School of the Arts, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- McMaster Institute for Music and the Mind, McMaster University, Hamilton, Ontario, Canada L8S 4K1
| | - Matthew H. Woolhouse
- School of the Arts, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- McMaster Institute for Music and the Mind, McMaster University, Hamilton, Ontario, Canada L8S 4K1
| | - Benjamin M. Bolker
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- Department of Biology, McMaster University, Hamilton, Ontario, Canada L8S 4K1
| | - David J. D. Earn
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- McMaster Institute for Music and the Mind, McMaster University, Hamilton, Ontario, Canada L8S 4K1
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35
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Chen Y, Liu F, Yu Q, Li T. Review of fractional epidemic models. APPLIED MATHEMATICAL MODELLING 2021; 97:281-307. [PMID: 33897091 PMCID: PMC8056944 DOI: 10.1016/j.apm.2021.03.044] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Revised: 03/04/2021] [Accepted: 03/23/2021] [Indexed: 05/10/2023]
Abstract
The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.
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Affiliation(s)
- Yuli Chen
- Fuzhou University Zhicheng College, Fujian 350001, China
| | - Fawang Liu
- School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
- College of Mathematics and Computer Science, Fuzhou University, Fujian 350116, China
| | - Qiang Yu
- School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
| | - Tianzeng Li
- School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
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36
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Ruiz-Herrera A, Torres PJ. The Role of Movement Patterns in Epidemic Models on Complex Networks. Bull Math Biol 2021; 83:98. [PMID: 34410514 PMCID: PMC8376740 DOI: 10.1007/s11538-021-00929-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 07/21/2021] [Indexed: 12/29/2022]
Abstract
In this paper, we analyze the influence of the usual movement variables on the spread of an epidemic. Specifically, given two spatial topologies, we can deduce which topology produces less infected individuals. In particular, we determine the topology that minimizes the overall number of infected individuals. It is worth noting that we do not assume any of the common simplifying assumptions in network theory such as all the links have the same diffusion rate or the movement of the individuals is symmetric. Our main conclusion is that the degree of mobility of the population plays a critical role in the spread of a disease. Finally, we derive theoretical insights to management of epidemics.
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Affiliation(s)
- Alfonso Ruiz-Herrera
- Department of Mathematics, Faculty of Science, University of Oviedo, Oviedo, Spain.
| | - Pedro J Torres
- Department of Applied Mathematics, Faculty of Science, University of Granada, Granada, Spain
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37
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Alternative transmission pathways for guinea worm in dogs: implications for outbreak risk and control. Int J Parasitol 2021; 51:1027-1034. [PMID: 34246634 DOI: 10.1016/j.ijpara.2021.05.005] [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: 02/16/2021] [Revised: 05/10/2021] [Accepted: 05/13/2021] [Indexed: 11/24/2022]
Abstract
Guinea worm (Dracunculus medinensis) has exerted a high human health burden in parts of Africa. Complete eradication of Guinea worm disease (dracunculiasis) may be delayed by the circulation of the parasite in domestic dogs. As with humans, dogs acquire the parasite by directly ingesting infected copepods, and recent evidence suggests that consuming frogs that ingested infected copepods as tadpoles may be a viable transmission route (paratenic route). To understand the relative contributions of direct and paratenic transmission routes, we developed a mathematical model that describes transmission of Guinea worm between dogs, copepods and frogs. We explored how the parasite basic reproductive number (R0) depends on parameters amenable to actionable interventions under three scenarios: frogs/tadpoles do not consume copepods; tadpoles consume copepods but frogs do not contribute to transmission; and frogs are paratenic hosts. We found a non-monotonic relationship between the number of dogs and R0. Generally, frogs can contribute to disease control by removing infected copepods from the waterbody even when paratenic transmission can occur. However, paratenic transmission could play an important role in maintaining the parasite when direct transmission is reduced by interventions focused on reducing copepod ingestion by dogs. Together, these suggest that the most effective intervention strategies may be those which focus on the reduction of copepods, as this reduces outbreak potential irrespective of the importance of the paratenic route.
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38
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Huo ZY, Lee DM, Wang S, Kim YJ, Kim SW. Emerging Energy Harvesting Materials and Devices for Self-Powered Water Disinfection. SMALL METHODS 2021; 5:e2100093. [PMID: 34927999 DOI: 10.1002/smtd.202100093] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Revised: 05/10/2021] [Indexed: 06/14/2023]
Abstract
Contaminated drinking water is one of the main pathogen transmission pathways making waterborne illnesses such as diarrheal diseases and gastroenteritis a huge threat to public health, especially in the areas where sanitation facilities and gird power are inadequate such as rural and disaster hit areas. Self-powered water disinfection systems are a promising solution in these cases. In this review paper, the authors provide an overview of the new and emerging methods of applying energy harvesting materials and devices as a source of power for water disinfection systems microbial disinfection in water by harnessing ambient forms of energy such as mechanical motion, light, and heat into electricity. The authors begin with a brief introduction of the different energy harvesting technologies commonly applied in water disinfection; triboelectric, piezoelectric, pyroelectric, and photovoltaic effects. Various microbial disinfection mechanisms and types of device construction are summarized. Then, a detailed discussion of the energy harvester-driven water disinfection process is provided. Finally, challenges and perspectives regarding the future development of self-powered water disinfection are described.
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Affiliation(s)
- Zheng-Yang Huo
- School of Advanced Materials Science and Engineering, Sungkyunkwan University (SKKU), Suwon, 16419, Republic of Korea
| | - Dong-Min Lee
- School of Advanced Materials Science and Engineering, Sungkyunkwan University (SKKU), Suwon, 16419, Republic of Korea
| | - Si Wang
- School of Advanced Materials Science and Engineering, Sungkyunkwan University (SKKU), Suwon, 16419, Republic of Korea
- School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China (UESTC), Chengdu, 610054, P. R. China
| | - Young-Jun Kim
- School of Advanced Materials Science and Engineering, Sungkyunkwan University (SKKU), Suwon, 16419, Republic of Korea
| | - Sang-Woo Kim
- School of Advanced Materials Science and Engineering, Sungkyunkwan University (SKKU), Suwon, 16419, Republic of Korea
- SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University (SKKU), Suwon, 16419, Republic of Korea
- Samsung Advanced Institute for Health Sciences & Technology (SAIHST), Sungkyunkwan University (SKKU), Suwon, 16419, Republic of Korea
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39
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Gandzha IS, Kliushnichenko OV, Lukyanets SP. Modeling and controlling the spread of epidemic with various social and economic scenarios. CHAOS, SOLITONS, AND FRACTALS 2021; 148:111046. [PMID: 34103789 PMCID: PMC8174143 DOI: 10.1016/j.chaos.2021.111046] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 05/06/2021] [Indexed: 06/12/2023]
Abstract
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe various scenarios of epidemic spreading. As compared to the basic SIR model, our model takes into account two possible routes of contagion transmission: direct from the infected compartment to the susceptible compartment and indirect via some intermediate medium or fomites. Transmission rates are estimated in terms of average distances between the individuals in selected social environments and characteristic time spans for which the individuals stay in each of these environments. We also introduce a collective economic resource associated with the average amount of money or income per individual to describe the socioeconomic interplay between the spreading process and the resource available to infected individuals. The epidemic-resource coupling is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. Our model brings an advantage of building various control strategies to mitigate the effect of epidemic and can be applied, in particular, to modeling the spread of COVID-19.
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Affiliation(s)
- I S Gandzha
- Institute of Physics, National Academy of Sciences of Ukraine, Prosp. Nauky 46, Kyiv 03028, Ukraine
| | - O V Kliushnichenko
- Institute of Physics, National Academy of Sciences of Ukraine, Prosp. Nauky 46, Kyiv 03028, Ukraine
| | - S P Lukyanets
- Institute of Physics, National Academy of Sciences of Ukraine, Prosp. Nauky 46, Kyiv 03028, Ukraine
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40
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Lata K, Misra AK, Takeuchi Y. Modeling the Effectiveness of TV and Social Media Advertisements on the Dynamics of Water-Borne Diseases. INT J BIOMATH 2021. [DOI: 10.1142/s1793524521500698] [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
Cholera is a serious threat to the health of human-kind all over the world and its control is a problem of great concern. In this context, a nonlinear mathematical model to control the prevalence of cholera disease is proposed and analyzed by incorporating TV and social media advertisements as a dynamic variable. It is considered that TV and social media ads propagate the knowledge among the people regarding the severe effects of cholera disease on human health along with its precautionary measures. It is also assumed that the mode of transmission of cholera disease among susceptible individuals is due to consumption of contaminated drinking water containing Vibrio cholerae. Moreover, the propagation of knowledge through TV and social media ads makes the people aware to adopt precautionary measures and also the aware people make some effectual efforts to washout the bacteria from the aquatic environment. Model analysis reveals that increase in the washout rate of bacteria due to aware individuals causes the stability switch. It is found that TV and social media ads have the potential to reduce the number of infectives in the region and thus control the cholera epidemic. Numerical simulation is performed for a particular set of parameter values to support the analytical findings.
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Affiliation(s)
- Kusum Lata
- Department of Mathematical & Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki 225 003, India
| | - A. K. Misra
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221 005, India
| | - Y. Takeuchi
- College of Science and Engineering, Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan
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41
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Chandrasekaran S, Jiang SC. A dose response model for Staphylococcus aureus. Sci Rep 2021; 11:12542. [PMID: 34131202 PMCID: PMC8206448 DOI: 10.1038/s41598-021-91822-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 05/31/2021] [Indexed: 11/11/2022] Open
Abstract
Dose-response models (DRMs) are used to predict the probability of microbial infection when a person is exposed to a given number of pathogens. In this study, we propose a new DRM for Staphylococcus aureus (SA), which causes skin and soft-tissue infections. The current approach to SA dose-response is only partially mechanistic and assumes that individual bacteria do not interact with each other. Our proposed two-compartment (2C) model assumes that bacteria that have not adjusted to the host environment decay. After adjusting to the host, they exhibit logistic/cooperative growth, eventually causing disease. The transition between the adjusted and un-adjusted states is a stochastic process, which the 2C DRM explicitly models to predict response probabilities. By fitting the 2C model to SA pathogenesis data, we show that cooperation between individual SA bacteria is sufficient (and, within the scope of the 2C model, necessary) to characterize the dose-response. This is a departure from the classical single-hit theory of dose-response, where complete independence is assumed between individual pathogens. From a quantitative microbial risk assessment standpoint, the mechanistic basis of the 2C DRM enables transparent modeling of dose-response of antibiotic-resistant SA that has not been possible before. It also enables the modeling of scenarios having multiple/non-instantaneous exposures, with minimal assumptions.
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Affiliation(s)
| | - Sunny C Jiang
- Civil and Environmental Engineering, University of California, Irvine, Irvine, 92697, USA
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42
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Memarbashi R, Mahmoudi SM. A dynamic model for the COVID-19 with direct and indirect transmission pathways. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2021; 44:5873-5887. [PMID: 33821067 PMCID: PMC8013540 DOI: 10.1002/mma.7154] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Revised: 12/12/2020] [Accepted: 12/13/2020] [Indexed: 05/31/2023]
Abstract
Two common transmission pathways for the spread of COVID-19 virus are direct and indirect. The direct pathway refers to the person-to-person transmission between susceptibles and infectious individuals. Infected individuals shed virus on the objects, and new infections arise through touching a contaminated surface; this refers to the indirect transmission pathway. We model the direct and indirect transmission pathways with a S A D O I R ode model. Our proposal explicitly includes compartments for the contaminated objects, susceptible individuals, asymptomatic infectious, detected infectious, and recovered individuals. We compute the basic reproduction number and epidemic growth rate of the model and determine how these fundamental quantities relate to the transmission rate of the pathways. We further study the relationship between the rate of loss of immunity and the occurrence of backward bifurcation. An efficient statistical framework is introduced to estimate the parameters of the model. We show the performance of the model in the simulation scenarios and the real data from the COVID-19 daily cases in South Korea.
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43
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Optimal Control Analysis of Cholera Dynamics in the Presence of Asymptotic Transmission. AXIOMS 2021. [DOI: 10.3390/axioms10020060] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Many mathematical models have explored the dynamics of cholera but none have been used to predict the optimal strategies of the three control interventions (the use of hygiene promotion and social mobilization; the use of treatment by drug/oral re-hydration solution; and the use of safe water, hygiene, and sanitation). The goal here is to develop (deterministic and stochastic) mathematical models of cholera transmission and control dynamics, with the aim of investigating the effect of the three control interventions against cholera transmission in order to find optimal control strategies. The reproduction number Rp was obtained through the next generation matrix method and sensitivity and elasticity analysis were performed. The global stability of the equilibrium was obtained using the Lyapunov functional. Optimal control theory was applied to investigate the optimal control strategies for controlling the spread of cholera using the combination of control interventions. The Pontryagin’s maximum principle was used to characterize the optimal levels of combined control interventions. The models were validated using numerical experiments and sensitivity analysis was done. Optimal control theory showed that the combinations of the control intervention influenced disease progression. The characterisation of the optimal levels of the multiple control interventions showed the means for minimizing cholera transmission, mortality, and morbidity in finite time. The numerical experiments showed that there are fluctuations and noise due to its dependence on the corresponding population size and that the optimal control strategies to effectively control cholera transmission, mortality, and morbidity was through the combinations of all three control interventions. The developed models achieved the reduction, control, and/or elimination of cholera through incorporating multiple control interventions.
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44
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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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45
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Botelho C, Dzevela Kong J, Ali Ber Lucien M, Shuai Z, Wang H. A mathematical model for Vibrio-phage interactions. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:2688-2712. [PMID: 33892567 DOI: 10.3934/mbe.2021137] [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: 06/12/2023]
Abstract
A cholera model has been formulated to incorporate the interaction of bacteria and phage. It is shown that there may exist three equilibria: one disease free and two endemic equilibria. Threshold parameters have been derived to characterize stability of these equilibria. Sensitivity analysis and disease control strategies have been employed to characterize the impact of bacteria-phage interaction on cholera dynamics.
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Affiliation(s)
- Christopher Botelho
- Department of Mathematics, University of Central Florida, Orlando, Florida, 32816, USA
| | - Jude Dzevela Kong
- Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada
- The Canadian Center for Disease Modelling, York University, Toronto, Ontario, M3J 1P3, Canada
| | - Mentor Ali Ber Lucien
- Laboratoire National de Santé Publique, Ministère de la Santé Publique et de la Population d'Haiti, Port-au-Prince, HT6120, Haiti
| | - Zhisheng Shuai
- Department of Mathematics, University of Central Florida, Orlando, Florida, 32816, USA
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
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46
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Sharma S, Singh F. Backward bifurcation in a cholera model with a general treatment function. SN APPLIED SCIENCES 2021. [DOI: 10.1007/s42452-021-04189-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
AbstractWe consider a general cholera model with a nonlinear treatment function. The treatment function describes the saturated treatment scenario due to the limited availability of resources. The sufficient conditions for the existence of backward bifurcation have been obtained using the central manifold theory. At last, we illustrate the results by considering some special types of treatment functions.
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McGahan I, Powell J, Spencer E. 28 Models Later: Model Competition and the Zombie Apocalypse. Bull Math Biol 2021; 83:22. [PMID: 33452943 PMCID: PMC7811353 DOI: 10.1007/s11538-020-00845-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 12/09/2020] [Indexed: 11/06/2022]
Abstract
Between Fall 2011 and Fall 2012 students at Utah State University played several rounds of Humans versus Zombies (HvZ), a role-playing variant of tag popular on college campuses. The goal of the game is for the zombies to tag humans, converting them into more zombies. Based on portrayals of 'zombieism' in popular culture, one might treat HvZ as a disease system. However, a traditional SIR model with mass-action dynamics does a poor job of modeling HvZ, leading to the natural question: What mechanisms drive the dynamics of the HvZ system? We use model competition, with Bayesian Information Criterion as arbiter, to answer this question. First, we develop a suite of models with a variety of transmission mechanisms and fit to data from fall 2011. We use model competition to determine which model(s) have the most support from the data, thereby offering insight into driving mechanisms for HvZ. Bootstrapping is used to both assess the significance of individual mechanisms and to determine confidence in the performance of our models. Finally, we test predictions of the best models with data from fall 2012. Results indicate that through both years of the game humans tend to cluster defensively, zombies tend to hunt in groups, some zombies are more proficient hunters, and some humans leave the game.
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Affiliation(s)
- Ian McGahan
- Department of Mathematics and Statistics, Utah State University, Logan, USA.
| | - James Powell
- Department of Mathematics and Statistics, Utah State University, Logan, USA
| | - Elizabeth Spencer
- Department of Statistics and Applied Probability, University of California Santa Barbara, Santa Barbara, USA
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Vishwakarma A, Lal R, Ramya M. Aptamer-based approaches for the detection of waterborne pathogens. Int Microbiol 2021; 24:125-140. [PMID: 33404933 DOI: 10.1007/s10123-020-00154-w] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Revised: 10/13/2020] [Accepted: 12/14/2020] [Indexed: 02/06/2023]
Abstract
Waterborne ailments pose a serious threat to public health and are a huge economic burden. Lack of hygiene in drinking and recreational water is the chief source of microbial pathogens in developing countries. Poor water quality and sanitation account for more than 3.4 million deaths a year worldwide. This has urged authorities and researchers to explore different avenues of pathogen detection. There is a growing demand for rapid and reliable sensor technologies, in particular those that can detect in situ and perform in harsh conditions. Some of the major waterborne pathogens include Vibrio cholerae, Leptospira interrogans, Campylobacter jejuni, Shigella spp., enterotoxigenic Escherichia coli, Clostridium difficile, Cryptosporidium parvum, Entamoeba histolytica, and Hepatitis A virus. While conventional methods of pathogen detection like serodiagnosis and microbiological methods have been superseded by nucleic acid amplification methods, there is still potential for improvement. This review provides an insight into aptamers and their utility in the form of aptasensors. It discusses how aptamer-based approaches have emerged as a novel strategy and its advantages over more resource-intensive and complex biochemical approaches.
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Affiliation(s)
- Archana Vishwakarma
- Molecular Genetics Laboratory, Department of Genetic Engineering, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Kanchipuram, Chennai, TN, India
| | - Roshni Lal
- Molecular Genetics Laboratory, Department of Genetic Engineering, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Kanchipuram, Chennai, TN, India
| | - Mohandass Ramya
- Molecular Genetics Laboratory, Department of Genetic Engineering, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Kanchipuram, Chennai, TN, India.
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Abstract
The article aims to estimate and forecast the transmissibility of shigellosis and explore the association of meteorological factors with shigellosis. The mathematical model named Susceptible–Exposed–Symptomatic/Asymptomatic–Recovered–Water/Food (SEIARW) was used to explore the feature of shigellosis transmission based on the data of Wuhan City, China, from 2005 to 2017. The study applied effective reproduction number (Reff) to estimate the transmissibility. Daily meteorological data from 2008 to 2017 were used to determine Spearman's correlation with reported new cases and Reff. The SEIARW model fit the data well (χ2 = 0.00046, p > 0.999). The simulation results showed that the reservoir-to-person transmission of the shigellosis route has been interrupted. The Reff would be reduced to a transmission threshold of 1.00 (95% confidence interval (CI) 0.82–1.19) in 2035. Reducing the infectious period to 11.25 days would also decrease the value of Reff to 0.99. There was a significant correlation between new cases of shigellosis and atmospheric pressure, temperature, wind speed and sun hours per day. The correlation coefficients, although statistically significant, were very low (<0.3). In Wuhan, China, the main transmission pattern of shigellosis is person-to-person. Meteorological factors, especially daily atmospheric pressure and temperature, may influence the epidemic of shigellosis.
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