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Anteneh LM, Lokonon BE, Kakaï RG. Modelling techniques in cholera epidemiology: A systematic and critical review. Math Biosci 2024; 373:109210. [PMID: 38777029 DOI: 10.1016/j.mbs.2024.109210] [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: 10/21/2023] [Revised: 05/09/2024] [Accepted: 05/13/2024] [Indexed: 05/25/2024]
Abstract
Diverse modelling techniques in cholera epidemiology have been developed and used to (1) study its transmission dynamics, (2) predict and manage cholera outbreaks, and (3) assess the impact of various control and mitigation measures. In this study, we carry out a critical and systematic review of various approaches used for modelling the dynamics of cholera. Also, we discuss the strengths and weaknesses of each modelling approach. A systematic search of articles was conducted in Google Scholar, PubMed, Science Direct, and Taylor & Francis. Eligible studies were those concerned with the dynamics of cholera excluding studies focused on models for cholera transmission in animals, socio-economic factors, and genetic & molecular related studies. A total of 476 peer-reviewed articles met the inclusion criteria, with about 40% (32%) of the studies carried out in Asia (Africa). About 52%, 21%, and 9%, of the studies, were based on compartmental (e.g., SIRB), statistical (time series and regression), and spatial (spatiotemporal clustering) models, respectively, while the rest of the analysed studies used other modelling approaches such as network, machine learning and artificial intelligence, Bayesian, and agent-based approaches. Cholera modelling studies that incorporate vector/housefly transmission of the pathogen are scarce and a small portion of researchers (3.99%) considers the estimation of key epidemiological parameters. Vaccination only platform was utilized as a control measure in more than half (58%) of the studies. Research productivity in cholera epidemiological modelling studies have increased in recent years, but authors used diverse range of models. Future models should consider incorporating vector/housefly transmission of the pathogen and on the estimation of key epidemiological parameters for the transmission of cholera dynamics.
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Affiliation(s)
- Leul Mekonnen Anteneh
- Laboratoire de Biomathématiques et d'Estimations Forestières, University of Abomey-Calavi, Cotonou, Benin.
| | - Bruno Enagnon Lokonon
- Laboratoire de Biomathématiques et d'Estimations Forestières, University of Abomey-Calavi, Cotonou, Benin
| | - Romain Glèlè Kakaï
- Laboratoire de Biomathématiques et d'Estimations Forestières, University of Abomey-Calavi, Cotonou, Benin
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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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Colombo A. The Basic Reproduction Number as a Loop Gain Matrix. IEEE CONTROL SYSTEMS LETTERS 2021; 6:199-204. [PMID: 35582631 PMCID: PMC8864943 DOI: 10.1109/lcsys.2021.3056616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Revised: 01/05/2021] [Accepted: 01/24/2021] [Indexed: 06/15/2023]
Abstract
The COVID-19 pandemic and the disordered reactions of most governments made the importance of mathematical modelling and model-based predictions evident, even outside the scientific community. The basic reproduction number [Formula: see text] quickly entered the common jargon, as a concise but effective tool to communicate the spreading power of a disease and estimate, at least roughly, the possible outcomes of the epidemic. However, while [Formula: see text] is easily defined for simple models, its proper definition is more subtle for larger, state-of-the-art models. Here we show that it is nothing else than the spectral radius of the gain matrix of a linear system, and that this matrix generalizes [Formula: see text] in the computation of the vector-valued final epidemic size and epidemic threshold, in a large class of finite-dimensional SIR-like models.
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Affiliation(s)
- A. Colombo
- Department of ElectronicsInformation, and BioengineeringPolitecnico di Milano20133MilanItaly
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Terefe YA, Kassa SM. Analysis of a mathematical model for the transmission dynamics of human melioidosis. INT J BIOMATH 2020. [DOI: 10.1142/s179352452050062x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number [Formula: see text] is less than one. It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse. The existence of backward bifurcation implies that bringing down [Formula: see text] to less than unity is not enough for disease eradication. In the absence of backward bifurcation, the global asymptotic stability of the disease-free equilibrium is shown whenever [Formula: see text]. For [Formula: see text], the existence of at least one locally asymptotically stable endemic equilibrium is shown. Sensitivity analysis of the model, using the parameters relevant to the transmission dynamics of the melioidosis disease, is discussed. Numerical experiments are presented to support the theoretical analysis of the model. In the numerical experimentations, it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.
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Affiliation(s)
- Yibeltal Adane Terefe
- Department of Mathematics and Applied Mathematics, University of Limpopo, South Africa
| | - Semu Mitiku Kassa
- Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana
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Meszaros VA, Miller-Dickson MD, Baffour-Awuah F, Almagro-Moreno S, Ogbunugafor CB. Direct transmission via households informs models of disease and intervention dynamics in cholera. PLoS One 2020; 15:e0229837. [PMID: 32163436 PMCID: PMC7067450 DOI: 10.1371/journal.pone.0229837] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 02/14/2020] [Indexed: 02/07/2023] Open
Abstract
While several basic properties of cholera outbreaks are common to most settings-the pathophysiology of the disease, the waterborne nature of transmission, and others-recent findings suggest that transmission within households may play a larger role in cholera outbreaks than previously appreciated. Important features of cholera outbreaks have long been effectively modeled with mathematical and computational approaches, but little is known about how variation in direct transmission via households may influence epidemic dynamics. In this study, we construct a mathematical model of cholera that incorporates transmission within and between households. We observe that variation in the magnitude of household transmission changes multiple features of disease dynamics, including the severity and duration of outbreaks. Strikingly, we observe that household transmission influences the effectiveness of possible public health interventions (e.g. water treatment, antibiotics, vaccines). We find that vaccine interventions are more effective than water treatment or antibiotic administration when direct household transmission is present. Summarizing, we position these results within the landscape of existing models of cholera, and speculate on its implications for epidemiology and public health.
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Affiliation(s)
- Victor A. Meszaros
- Department of Ecology and Evolutionary Biology, Brown University, Providence, RI, United States of America
| | - Miles D. Miller-Dickson
- Department of Ecology and Evolutionary Biology, Brown University, Providence, RI, United States of America
| | - Francis Baffour-Awuah
- Department of Mathematics, Florida State University, Tallahassee, FL, United States of America
| | - Salvador Almagro-Moreno
- Burnett School of Biomedical Sciences, University of Central Florida, Orlando, FL, United States of America
- National Center for Integrated Coastal Research, University of Central Florida, Orlando, FL, United States of America
| | - C. Brandon Ogbunugafor
- Department of Ecology and Evolutionary Biology, Brown University, Providence, RI, United States of America
- * E-mail:
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Miller-Dickson MD, Meszaros VA, Almagro-Moreno S, Brandon Ogbunugafor C. Hepatitis C virus modelled as an indirectly transmitted infection highlights the centrality of injection drug equipment in disease dynamics. J R Soc Interface 2019; 16:20190334. [PMID: 31480919 PMCID: PMC6769301 DOI: 10.1098/rsif.2019.0334] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Accepted: 08/05/2019] [Indexed: 01/05/2023] Open
Abstract
The hepatitis C virus (HCV) epidemic often occurs through the persistence of injection drug use. Mathematical models have been useful in understanding various aspects of the HCV epidemic, and especially, the importance of new treatment measures. Until now, however, few models have attempted to understand HCV in terms of an interaction between the various actors in an HCV outbreak-hosts, viruses and the needle injection equipment. In this study, we apply perspectives from the ecology of infectious diseases to model the transmission of HCV among a population of injection drug users. The products of our model suggest that modelling HCV as an indirectly transmitted infection-where the injection equipment serves as an environmental reservoir for infection-facilitates a more nuanced understanding of disease dynamics, by animating the underappreciated actors and interactions that frame disease. This lens may allow us to understand how certain public health interventions (e.g. needle exchange programmes) influence HCV epidemics. Lastly, we argue that this model is of particular importance in the light of the modern opioid epidemic, which has already been associated with outbreaks of viral diseases.
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Affiliation(s)
| | - Victor A. Meszaros
- Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02906, USA
| | - Salvador Almagro-Moreno
- Burnett School of Biomedical Sciences, University of Central Florida, Orlando, FL 32827, USA
- National Center for Integrated Coastal Research, University of Central Florida, Orlando, FL 32816, USA
| | - C. Brandon Ogbunugafor
- Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02906, USA
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Jacobsen KA, Burch MG, Tien JH, Rempała GA. The large graph limit of a stochastic epidemic model on a dynamic multilayer network. JOURNAL OF BIOLOGICAL DYNAMICS 2018; 12:746-788. [PMID: 30175687 DOI: 10.1080/17513758.2018.1515993] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Accepted: 08/17/2018] [Indexed: 06/08/2023]
Abstract
We consider a Markovian SIR-type (Susceptible → Infected → Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model where edges in different layers correspond to potentially infectious contacts of different types. We assume that the graph structure evolves in response to the epidemic via activation or deactivation of edges of infectious nodes. We derive a large graph limit theorem that gives a system of ordinary differential equations (ODEs) describing the evolution of quantities of interest, such as the proportions of infected and susceptible vertices, as the number of nodes tends to infinity. Analysis of the limiting system elucidates how the coupling of edge activation and deactivation to infection status affects disease dynamics, as illustrated by a two-layer network example with edge types corresponding to community and healthcare contacts. Our theorem extends some earlier results describing the deterministic limit of stochastic SIR processes on static, single-layer configuration model graphs. We also describe precisely the conditions for equivalence between our limiting ODEs and the systems obtained via pair approximation, which are widely used in the epidemiological and ecological literature to approximate disease dynamics on networks. The flexible modeling framework and asymptotic results have potential application to many disease settings including Ebola dynamics in West Africa, which was the original motivation for this study.
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Affiliation(s)
- Karly A Jacobsen
- a College of Public Health, Department of Mathematics and Mathematical Biosciences Institute , The Ohio State University , Columbus , OH , USA
| | - Mark G Burch
- a College of Public Health, Department of Mathematics and Mathematical Biosciences Institute , The Ohio State University , Columbus , OH , USA
| | - Joseph H Tien
- a College of Public Health, Department of Mathematics and Mathematical Biosciences Institute , The Ohio State University , Columbus , OH , USA
| | - Grzegorz A Rempała
- a College of Public Health, Department of Mathematics and Mathematical Biosciences Institute , The Ohio State University , Columbus , OH , USA
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Wang Y, Ma J, Cao J, Li L. Edge-based epidemic spreading in degree-correlated complex networks. J Theor Biol 2018; 454:164-181. [PMID: 29885412 DOI: 10.1016/j.jtbi.2018.06.006] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2018] [Revised: 06/03/2018] [Accepted: 06/05/2018] [Indexed: 10/14/2022]
Abstract
Networks that grow through the addition of new nodes or edges may acquire degree-degree correlations. When one considers a short epidemic on a slowly growing network, such as the spread of a strain of influenza in a population for one season, it is reasonable to assume that the degree-correlated network is static during the course of an epidemic. In this case using only information about the network degree distribution is not enough to capture the exponential growth phase, the epidemic peak or the final epidemic size. Hence, in this paper we formulate an edge-based SIR epidemic model on degree-correlated networks, which includes the Miller model on configuration networks as a special case. The model is relatively low-dimensional; in particular, considering the fact that it captures degree correlations. Moreover, we derive rate equations to compute two node degree correlations in a growing network. Predictions of our model agree well with the corresponding stochastic SIR process on degree-correlated networks, such as the exponential growth phase, the epidemic peak and the final epidemic size. The basic reproduction number R0 and the final epidemic size are theoretically derived, which are equivalent to those based on the percolation theory. However, our model has the advantage that it can trace the dynamic spread of an epidemic on degree-correlated networks. This provides us with more accurate information to predict and control the spread of diseases in growing populations with biased-mixing. Finally, our model is tested on degree-correlated networks with clustering, and it is shown that our model is robust to degree-correlated networks with small clustering.
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Affiliation(s)
- Yi Wang
- School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, People's Republic of China; School of Mathematics, Southeast University, Nanjing, Jiangsu 210096, People's Republic of China.
| | - Junling Ma
- Department of Mathematics and Statistics, University of Victoria, Victoria BC V8W 3R4, Canada.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing, Jiangsu 210096, People's Republic of China.
| | - Li Li
- School of Computer and Information Technology, Shanxi University, Taiyuan 030006, People's Republic of China
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An edge-based SIR model for sexually transmitted diseases on the contact network. J Theor Biol 2017; 439:216-225. [PMID: 29241662 DOI: 10.1016/j.jtbi.2017.12.003] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2017] [Revised: 11/22/2017] [Accepted: 12/01/2017] [Indexed: 11/21/2022]
Abstract
Sexually transmitted diseases, which are infections through sexual contact, pose severe public health threat nowadays. In this paper, we develop a novel model for such diseases on a bipartite random contact network. Our model is precise with arbitrary initial conditions, which makes it suitable to study preventative vaccination strategies. We derive the reproduction number and show that R0=1 is the disease threshold. An implicit formula for the final epidemic size is also derived, and we show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We find that the final size in either sex is heavily influenced by the degree distribution of the opposite sex.
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Willem L, Verelst F, Bilcke J, Hens N, Beutels P. Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015). BMC Infect Dis 2017; 17:612. [PMID: 28893198 PMCID: PMC5594572 DOI: 10.1186/s12879-017-2699-8] [Citation(s) in RCA: 72] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2016] [Accepted: 08/22/2017] [Indexed: 02/18/2023] Open
Abstract
Background Individual-based models (IBMs) are useful to simulate events subject to stochasticity and/or heterogeneity, and have become well established to model the potential (re)emergence of pathogens (e.g., pandemic influenza, bioterrorism). Individual heterogeneity at the host and pathogen level is increasingly documented to influence transmission of endemic diseases and it is well understood that the final stages of elimination strategies for vaccine-preventable childhood diseases (e.g., polio, measles) are subject to stochasticity. Even so it appears IBMs for both these phenomena are not well established. We review a decade of IBM publications aiming to obtain insights in their advantages, pitfalls and rationale for use and to make recommendations facilitating knowledge transfer within and across disciplines. Methods We systematically identified publications in Web of Science and PubMed from 2006-2015 based on title/abstract/keywords screening (and full-text if necessary) to retrieve topics, modeling purposes and general specifications. We extracted detailed modeling features from papers on established vaccine-preventable childhood diseases based on full-text screening. Results We identified 698 papers, which applied an IBM for infectious disease transmission, and listed these in a reference database, describing their general characteristics. The diversity of disease-topics and overall publication frequency have increased over time (38 to 115 annual publications from 2006 to 2015). The inclusion of intervention strategies (8 to 52) and economic consequences (1 to 20) are increasing, to the detriment of purely theoretical explorations. Unfortunately, terminology used to describe IBMs is inconsistent and ambiguous. We retrieved 24 studies on a vaccine-preventable childhood disease (covering 7 different diseases), with publication frequency increasing from the first such study published in 2008. IBMs have been useful to explore heterogeneous between- and within-host interactions, but combined applications are still sparse. The amount of missing information on model characteristics and study design is remarkable. Conclusions IBMs are suited to combine heterogeneous within- and between-host interactions, which offers many opportunities, especially to analyze targeted interventions for endemic infections. We advocate the exchange of (open-source) platforms and stress the need for consistent “branding”. Using (existing) conventions and reporting protocols would stimulate cross-fertilization between research groups and fields, and ultimately policy making in decades to come. Electronic supplementary material The online version of this article (doi:10.1186/s12879-017-2699-8) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Lander Willem
- Centre for Health Economics Research & Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium.
| | - Frederik Verelst
- Centre for Health Economics Research & Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
| | - Joke Bilcke
- Centre for Health Economics Research & Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
| | - Niel Hens
- Centre for Health Economics Research & Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium.,Interuniversity Institute for Biostatistics and statistical Bioinformatics, UHasselt, Hasselt, Belgium
| | - Philippe Beutels
- Centre for Health Economics Research & Modeling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium.,School of Public Health and Community Medicine, The University of New South Wales, Sydney, Australia
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van den Driessche P. Reproduction numbers of infectious disease models. Infect Dis Model 2017; 2:288-303. [PMID: 29928743 PMCID: PMC6002118 DOI: 10.1016/j.idm.2017.06.002] [Citation(s) in RCA: 188] [Impact Index Per Article: 26.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Revised: 06/23/2017] [Accepted: 06/26/2017] [Indexed: 12/29/2022] Open
Abstract
This primer article focuses on the basic reproduction number, ℛ 0 , for infectious diseases, and other reproduction numbers related to ℛ 0 that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of ℛ 0 determining whether or not the disease dies out. The next generation matrix method of calculating ℛ 0 in a compartmental model is described and illustrated. To address control strategies, type and target reproduction numbers are defined, as well as sensitivity and elasticity indices. These theoretical ideas are then applied to models that are formulated for West Nile virus in birds (a vector-borne disease), cholera in humans (a disease with two transmission pathways), anthrax in animals (a disease that can be spread by dead carcasses and spores), and Zika in humans (spread by mosquitoes and sexual contacts). Some parameter values from literature data are used to illustrate the results. Finally, references for other ways to calculate ℛ 0 are given. These are useful for more complicated models that, for example, take account of variations in environmental fluctuation or stochasticity.
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