Influence of human behavior on cholera dynamics

A Coupled Spatial-Network Model: A Mathematical Framework for Applications in Epidemiology

There is extensive evidence that network structure (e.g., air transport, rivers, or roads) may significantly enhance the spread of epidemics into the surrounding geographical area. A new compartmental modeling framework is proposed which couples well-mixed (ODE in time) population centers at the vertices, 1D travel routes on the graph's edges, and a 2D continuum containing the rest of the population to simulate how an infection spreads through a population. The edge equations are coupled to the vertex ODEs through junction conditions, while the domain equations are coupled to the edges through boundary conditions. A numerical method based on spatial finite differences for the edges and finite elements in the 2D domain is described to approximate the model, and numerical verification of the method is provided. The model is illustrated on two simple and one complex example geometries, and a parameter study example is performed. The observed solutions exhibit exponential decay after a certain time has passed, and the cumulative infected population over the vertices, edges, and domain tends to a constant in time but varying in space, i.e., a steady state solution.

Modelling techniques in cholera epidemiology: A systematic and critical review

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.

Effects of behaviour change on HFMD transmission

We propose a hand, foot and mouth disease (HFMD) transmission model for children with behaviour change and imperfect quarantine. The symptomatic and quarantined states obey constant behaviour change while others follow variable behaviour change depending on the numbers of new and recent infections. The basic reproduction number R 0 of the model is defined and shown to be a threshold for disease persistence and eradication. Namely, the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 whereas the disease persists and there is a unique endemic equilibrium otherwise. By fitting the model to weekly HFMD data of Shanghai in 2019, the reproduction number is estimated at 2.41. Sensitivity analysis for R 0 shows that avoiding contagious contacts and implementing strict quarantine are essential to lower HFMD persistence. Numerical simulations suggest that strong behaviour change not only reduces the peak size and endemic level dramatically but also impairs the role of asymptomatic transmission.

Global Hopf bifurcation of a cholera model with media coverage

We propose a model for cholera under the impact of delayed mass media, including human-to-human and environment-to-human transmission routes. First, we establish the extinction and uniform persistence of the disease with respect to the basic reproduction number. Then, we conduct a local and global Hopf bifurcation analysis by treating the delay as a bifurcation parameter. Finally, we carry out numerical simulations to demonstrate theoretical results. The impact of the media with the time delay is found to not influence the threshold dynamics of the model, but is a factor that induces periodic oscillations of the disease.

A two-phase fluid model for epidemic flow

We propose a new mathematical and computational modeling framework that incorporates fluid dynamics to study the spatial spread of infectious diseases. We model the susceptible and infected populations as two inviscid fluids which interact with each other. Their motion at the macroscopic level characterizes the progression and spread of the epidemic. To implement the two-phase flow model, we employ high-order numerical methods from computational fluid dynamics. We apply this model to simulate the COVID-19 outbreaks in the city of Wuhan in China and the state of Tennessee in the US. Our modeling and simulation framework allows us to conduct a detailed investigation into the complex spatiotemporal dynamics related to the transmission and spread of COVID-19.

Role of media coverage in a SVEIR-I epidemic model with nonlinear incidence and spatial heterogeneous environment

In this paper, we propose a SVEIR-I epidemic model with media coverage in a spatially heterogeneous environment, and study the role of media coverage in the spread of diseases in a spatially heterogeneous environment. In a spatially heterogeneous environment, we first set up the well-posedness of the model. Then, we define the basic reproduction number $ R_0 $ of the model and establish the global dynamic threshold criteria: when $ R_0 < 1 $, disease-free steady state is globally asymptotically stable, while when $ R_0 > 1 $, the model is uniformly persistent. In addition, the existence and uniqueness of the equilibrium state of endemic diseases were obtained when $ R_0 > 1 $ in homogeneous space and heterogeneous diffusion environment. Further, by constructing appropriate Lyapunov functions, the global asymptotic stability of disease-free and positive steady states was established. Finally, through numerical simulations, it is shown that spatial heterogeneity can increase the risk of disease transmission, and can even change the threshold for disease transmission; media coverage can make people more widely understand disease information, and then reduce the effective contact rate to control the spread of disease.

Computation of the basic reproduction numbers for reaction-diffusion epidemic models

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.

Influence of Human Behavior on COVID-19 Dynamics Based on a Reaction-Diffusion Model

To investigate the influence of human behavior on the spread of COVID-19, we propose a reaction-diffusion model that incorporates contact rate functions related to human behavior. The basic reproduction number R 0 is derived and a threshold-type result on its global dynamics in terms of R 0 is established. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 ; while there exists a positive stationary solution and the disease is uniformly persistent if R 0 > 1 . By the numerical simulations of the analytic results, we find that human behavior changes may lower infection levels and reduce the number of exposed and infected humans.

Mathematical Models for Cholera Dynamics-A Review

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.

Modeling the impact of precautionary measures and sanitation practices broadcasted through media on the dynamics of bacterial diseases

The media has a significant contribution in spreading awareness by broadcasting various programs about prevalent diseases in the society along with the role of providing information, feeding news and educating a large mass. In this paper, the effect of media programs promoting precautionary measures and sanitation practices to control the bacterial infection in the community is modeled and analyzed considering the number of media programs as a dynamical variable. In the modeling phenomena, human population is partitioned into three classes; susceptible, infected and recovered. The disease is supposed to spread by direct contact of susceptible with infected individuals and indirectly by the ingestion of bacteria present in the environment. The growth in the media programs is considered proportional to the size of infected population and the impact of these programs on the indirect disease transmission rate and bacteria shedding rate by infected individuals is also considered. The feasibility of equilibria and their stability conditions are obtained. Model analysis reveals that broadcasting media programs and increasing its effectiveness shrink the size of infected class and control the spread of disease to a large extent.

Mobility was a significant determinant of reported COVID-19 incidence during the Omicron Surge in the most populous U.S. Counties

BACKGROUND

Significant immune escape by the Omicron variant, along with the emergence of widespread worry fatigue, have called into question the robustness of the previously observed relation between population mobility and COVID-19 incidence.

METHODS

We employed principal component analysis to construct a one-dimensional summary indicator of six Google mobility categories. We related this mobility indicator to case incidence among 111 of the most populous U.S. counties during the Omicron surge from December 2021 through February 2022.

RESULTS

Reported COVID-19 incidence peaked earlier and declined more rapidly among those counties exhibiting more extensive decline in mobility between December 20 and January 3. Based upon a fixed-effects, longitudinal cohort model, we estimated that every 1% decline in mobility between December 20 and January 3 was associated with a 0.63% decline in peak incidence during the week ending January 17 (95% confidence interval, 0.40-0.86%). Based upon a cross-sectional analysis including mean household size and vaccination participation as covariates, we estimated that the same 1% decline in mobility was associated with a 0.36% decline in cumulative reported COVID-19 incidence from January 10 through February 28 (95% CI, 0.18-0.54%).

CONCLUSION

Omicron did not simply sweep through the U.S. population until it ran out of susceptible individuals to infect. To the contrary, a significant fraction managed to avoid infection by engaging in risk-mitigating behaviors. More broadly, the behavioral response to perceived risk should be viewed as an intrinsic component of the natural course of epidemics in humans.

Effects of human mobility and behavior on disease transmission in a COVID-19 mathematical model

Human interactions and perceptions about health risk are essential to understand the evolution over the course of a pandemic. We present a Susceptible-Exposed-Asymptomatic-Infectious-Recovered-Susceptible mathematical model with quarantine and social-distance-dependent transmission rates, to study COVID-19 dynamics. Human activities are split across different location settings: home, work, school, and elsewhere. Individuals move from home to the other locations at rates dependent on their epidemiological conditions and maintain a social distancing behavior, which varies with their location. We perform simulations and analyze how distinct social behaviors and restrictive measures affect the dynamic of the disease within a population. The model proposed in this study revealed that the main focus on the transmission of COVID-19 is attributed to the “home” location setting, which is understood as family gatherings including relatives and close friends. Limiting encounters at work, school and other locations will only be effective if COVID-19 restrictions occur simultaneously at all those locations and/or contact tracing or social distancing measures are effectively and strictly implemented, especially at the home setting.

Adding a reaction-restoration type transmission rate dynamic-law to the basic SEIR COVID-19 model

The classical SEIR model, being an autonomous system of differential equations, has important limitations when representing a pandemic situation. Particularly, the geometric unimodal shape of the epidemic curve is not what is generally observed. This work introduces the βSEIR model, which adds to the classical SEIR model a differential law to model the variation in the transmission rate. It considers two opposite thrives generally found in a population: first, reaction to disease presence that may be linked to mitigation strategies, which tends to decrease transmission, and second, the urge to return to normal conditions that pulls to restore the initial value of the transmission rate. Our results open a wide spectrum of dynamic variabilities in the curve of new infected, which are justified by reaction and restoration thrives that affect disease transmission over time. Some of these dynamics have been observed in the existing COVID-19 disease data. In particular and to further exemplify the potential of the model proposed in this article, we show its capability of capturing the evolution of the number of new confirmed cases of Chile and Italy for several months after epidemic onset, while incorporating a reaction to disease presence with decreasing adherence to mitigation strategies, as well as a seasonal effect on the restoration of the initial transmissibility conditions.

Modeling epidemic flow with fluid dynamics

In this paper, a new mathematical model based on partial differential equations is proposed to study the spatial spread of infectious diseases. The model incorporates fluid dynamics theory and represents the epidemic spread as a fluid motion generated through the interaction between the susceptible and infected hosts. At the macroscopic level, the spread of the infection is modeled as an inviscid flow described by the Euler equation. Nontrivial numerical methods from computational fluid dynamics (CFD) are applied to investigate the model. In particular, a fifth-order weighted essentially non-oscillatory (WENO) scheme is employed for the spatial discretization. As an application, this mathematical and computational framework is used in a simulation study for the COVID-19 outbreak in Wuhan, China. The simulation results match the reported data for the cumulative cases with high accuracy and generate new insight into the complex spatial dynamics of COVID-19.

Modelling the Role of Human Behaviour in Ebola Virus Disease (EVD) Transmission Dynamics

The role of human behaviour in the dynamics of infectious diseases cannot be underestimated. A clear understanding of how human behaviour influences the spread of infectious diseases is critical in establishing and designing control measures. To study the role that human behaviour plays in Ebola disease dynamics, in this paper, we design an Ebola virus disease model with disease transmission dynamics based on a new exponential nonlinear incidence function. This new incidence function that captures the reduction in disease transmission due to human behaviour innovatively considers the efficacy and the speed of behaviour change. The model's steady states are determined and suitable Lyapunov functions are built. The proofs of the global stability of equilibrium points are presented. To demonstrate the utility of the model, we fit the model to Ebola virus disease data from Liberia and Sierra Leone. The results which are comparable to existing findings from the outbreak of 2014 − 2016 show a better fit when the efficacy and the speed of behaviour change are higher. A rapid and efficacious behaviour change as a control measure to rapidly control an Ebola virus disease epidemic is advocated. Consequently, this model has implications for the management and control of future Ebola virus disease outbreaks.

How does handwashing behaviour change in response to a cholera outbreak? A qualitative case study in the Democratic Republic of the Congo

Background

Handwashing with soap has the potential to curb cholera transmission. This research explores how populations experienced and responded to the 2017 cholera outbreak in the Democratic Republic of the Congo and how this affected their handwashing behaviour.

Methods

Cholera cases were identified through local cholera treatment centre records. Comparison individuals were recruited from the same neighbourhoods by identifying households with no recent confirmed or suspected cholera cases. Multiple qualitative methods were employed to understand hand hygiene practices and their determinants, including unstructured observations, interviews and focus group discussions. The data collection tools and analysis were informed by the Behaviour Centred Design Framework. Comparisons were made between the experiences and practices of people from case households and participants from comparison households.

Results

Cholera was well understood by the population and viewed as a persistent and common health challenge. Handwashing with soap was generally observed to be rare during the outbreak despite self-reported increases in behaviour. Across case and comparison groups, individuals were unable to prioritise handwashing due to competing food-scarcity and livelihood challenges and there was little in the physical or social environments to cue handwashing or make it a convenient, rewarding or desirable to practice. The ability of people from case households to practice handwashing was further constrained by their exposure to cholera which in addition to illness, caused profound non-health impacts to household income, productivity, social status, and their sense of control.

Conclusions

Even though cholera outbreaks can cause disruptions to many determinants of behaviour, these shifts do not automatically facilitate an increase in preventative behaviours like handwashing with soap. Hygiene programmes targeting outbreaks within complex crises could be strengthened by acknowledging the emic experiences of the disease and adopting sustainable solutions which build upon local disease coping mechanisms.

A reaction-advection-diffusion model of cholera epidemics with seasonality and human behavior change

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.

Evidence-Based Health Behavior Interventions for Cholera: Lessons from an Outbreak Investigation in India

In rural India, since 2014, the Swachh Bharat Abhiyan (Clean India Mission) has ensured construction of more than 100 million toilets and is now focusing on reinforcement of sanitation behaviors. We report a cholera outbreak in a remote village in western India where open defecation was implicated in causation. A water pipeline was damaged in the vicinity of a stream flowing from a site of open defecation. Despite the availability of a toilet facility in the majority of households (75%), open defecation was widely practiced (62.8%). Many reported not washing hands with soap and water before eating (78.5%) and after defecation (61.1%). The study emphasizes the need for focused health behavior studies and evidence-based interventions to reduce the occurrence of cholera outbreaks. This could be the last lap in the path toward achieving the United Nations Sustainable Development Goal 6, which aims to "ensure availability and sustainable management of water and sanitation for all."

A spatial epidemic model with a moving boundary

We present a new mathematical model to investigate the spatial spread of an infectious disease. The model consists of a nonlinear PDE system with an unknown velocity field, defined on an epidemic domain that changes with time. The moving boundary of the domain represents the wavefront of the epidemic. We conduct an equilibrium analysis to the simplified models represented by ODE systems. We also perform a numerical study on the original PDE system for a range of scenarios, including one under a realistic epidemic setting.

A Review of the Environmental Trigger and Transmission Components for Prediction of Cholera

Climate variables influence the occurrence, growth, and distribution of Vibrio cholerae in the aquatic environment. Together with socio-economic factors, these variables affect the incidence and intensity of cholera outbreaks. The current pandemic of cholera began in the 1960s, and millions of cholera cases are reported each year globally. Hence, cholera remains a significant health challenge, notably where human vulnerability intersects with changes in hydrological and environmental processes. Cholera outbreaks may be epidemic or endemic, the mode of which is governed by trigger and transmission components that control the outbreak and spread of the disease, respectively. Traditional cholera risk assessment models, namely compartmental susceptible-exposed-infected-recovered (SEIR) type models, have been used to determine the predictive spread of cholera through the fecal–oral route in human populations. However, these models often fail to capture modes of infection via indirect routes, such as pathogen movement in the environment and heterogeneities relevant to disease transmission. Conversely, other models that rely solely on variability of selected environmental factors (i.e., examine only triggers) have accomplished real-time outbreak prediction but fail to capture the transmission of cholera within impacted populations. Since the mode of cholera outbreaks can transition from epidemic to endemic, a comprehensive transmission model is needed to achieve timely and reliable prediction with respect to quantitative environmental risk. Here, we discuss progression of the trigger module associated with both epidemic and endemic cholera, in the context of the autochthonous aquatic nature of the causative agent of cholera, V. cholerae, as well as disease prediction.

An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors

Modeling human behavior within mathematical models of infectious diseases is a key component to understand and control disease spread. We present a mathematical compartmental model of Susceptible-Infectious-Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on the distance that individuals keep on average to others in their daily lives. We assume that this distance varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present simulations to compare results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior, such as: the reaction velocity of a society to change social distance during an epidemic. We observe the vulnerability to disease spread of close contact societies, and also show that certain social distancing behavior may provoke a small peak of a first epidemic outbreak, but at the expense of it occurring early after the epidemic onset, observing differences in this regard between society types. We also discuss the appearance of temporal oscillations of the four different transmission rates, their differences, and how this oscillatory behavior is impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.

COVID-19 early-alert signals using human behavior alternative data

Google searches create a window into population-wide thoughts and plans not just of individuals, but populations at large. Since the outbreak of COVID-19 and the non-pharmaceutical interventions introduced to contain it, searches for socially distanced activities have trended. We hypothesize that trends in the volume of search queries related to activities associated with COVID-19 transmission correlate with subsequent COVID-19 caseloads. We present a preliminary analytics framework that examines the relationship between Google search queries and the number of newly confirmed COVID-19 cases in the United States. We designed an experimental tool with search volume indices to track interest in queries related to two themes: isolation and mobility. Our goal was to capture the underlying social dynamics of an unprecedented pandemic using alternative data sources that are new to epidemiology. Our results indicate that the net movement index we defined correlates with COVID-19 weekly new case growth rate with a lag of between 10 and 14 days for the United States at-large, as well as at the state level for 42 out of 50 states with the exception of 8 states (DE, IA, KS, NE, ND, SD, WV, WY) from March to June 2020. In addition, an increasing caseload was seen over the summer in some southern US states. A sharp rise in mobility indices was followed by a sharp increase, respectively, in the case growth data, as seen in our case study of Arizona, California, Florida, and Texas. A sharp decline in mobility indices is often followed by a sharp decline, respectively, in the case growth data, as seen in our case study of Arizona, California, Florida, Texas, and New York. The digital epidemiology framework presented here aims to discover predictors of the pandemic's curve, which could supplement traditional predictive models and inform early warning systems and public health policies.

MODELING CHOLERA TRANSMISSION UNDER DISEASE CONTROL MEASURES

We present a new mathematical model to investigate the transmission dynamics of cholera under disease control measures that include education programs and water sanitation. The model incorporates the impact of education programs into the disease transmission rates and that of water sanitation into the environmental pathogen dynamics. We conduct a detailed analysis to the autonomous system of the model and establish the local and global stabilities of its equilibria that characterize the threshold dynamics of cholera. We then perform an optimal control study on the general model with time-dependent controls and explore effective approaches to implement the education programs and water sanitation while balancing their costs. Our analysis and simulation highlight the complex interaction among the direct and indirect transmission pathways of the disease, the intrinsic growth of the environmental pathogen and the impact of multiple control measures, and their roles in collectively shaping the transmission dynamics of cholera.

Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models

We study the basic reproduction numbers for a class of reaction-diffusion epidemic models that are developed from autonomous ODE systems. We present a general numerical framework to compute such basic reproduction numbers; meanwhile, the numerical formulation provides useful insight into their characterizations. Using matrix analysis, we show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important cases that include, among others, a single infected compartment, constant diffusion rates, uniform diffusion patterns among the infected compartments, and partial diffusion in the system.

Modelling cholera transmission dynamics in the presence of limited resources

Objectives

We study the transmission dynamics of cholera in the presence of limited resources, a common feature of the developing world. The model is used to gain insight into the impact of available resources of the health care system on the spread and control of the disease. A deterministic model that includes a nonlinear recovery rate is formulated and rigorously analyzed. Limited treatment is described by inclusion of a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings.

Results

The model analysis shows that the disease free steady state is locally stable when the threshold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0} < 1$$\end{document}R0<1. It is also shown that the model has multiple equilibria and the model exhibits the phenomenon of backward bifurcation whose implications to cholera infection are discussed. The results are useful for the public health planning in resource allocation for the control of cholera transmission.

A CHOLERA METAPOPULATION MODEL INTERLINKING MIGRATION WITH INTERVENTION STRATEGIES — A CASE STUDY OF ZIMBABWE (2008–2009)

Cholera is a water-borne disease and a major threat to human society affecting about 3–5 million people annually. A considerable number of research works have already been done to understand the disease transmission route and preventive measures in spatial or non-spatial scale. However, how the control strategies are to be linked up with the human migration in different locations in a country are not well studied. The present investigation is carried out in this direction by proposing and analyzing cholera meta-population models. The basic dynamical properties including the domain basic reproduction number are studied. Several important model parameters are estimated using cholera incidence data (2008–2009) and inter-provincial migration data from Census 2012 for the five provinces in Zimbabwe. By defining some migration index, and interlinking these indices with different cholera control strategies, namely, promotion of hand-hygiene and clean water supply and treatment, we carried out an optimal cost effectiveness analysis using optimal control theory. Our analysis suggests that there is no need to provide control measures for all the five provinces, and the control measures should be provided only to those provinces where in-migration flow is moderate. We also observe that such selective control measures which are also cost effective may reduce the overall cases and deaths.

A multi-scale cholera model linking between-host and within-host dynamics

We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host level, we describe the evolution of the pathogen within the human body. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for our model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics.

Modeling the within-host dynamics of cholera: bacterial-viral interaction

Novel deterministic and stochastic models are proposed in this paper for the within-host dynamics of cholera, with a focus on the bacterial-viral interaction. The deterministic model is a system of differential equations describing the interaction among the two types of vibrios and the viruses. The stochastic model is a system of Markov jump processes that is derived based on the dynamics of the deterministic model. The multitype branching process approximation is applied to estimate the extinction probability of bacteria and viruses within a human host during the early stage of the bacterial-viral infection. Accordingly, a closed-form expression is derived for the disease extinction probability, and analytic estimates are validated with numerical simulations. The local and global dynamics of the bacterial-viral interaction are analysed using the deterministic model, and the result indicates that there is a sharp disease threshold characterized by the basic reproduction number [Formula: see text]: if [Formula: see text], vibrios ingested from the environment into human body will not cause cholera infection; if [Formula: see text], vibrios will grow with increased toxicity and persist within the host, leading to human cholera. In contrast, the stochastic model indicates, more realistically, that there is always a positive probability of disease extinction within the human host.

Impact of Awareness Programs on Cholera Dynamics: Two Modeling Approaches

We propose two differential equation-based models to investigate the impact of awareness programs on cholera dynamics. The first model represents the disease transmission rates as decreasing functions of the number of awareness programs, whereas the second model divides the susceptible individuals into two distinct classes depending on their awareness/unawareness of the risk of infection. We study the essential dynamical properties of each model, using both analytical and numerical approaches. We find that the two models, though closely related, exhibit significantly different dynamical behaviors. Namely, the first model follows regular threshold dynamics while rich dynamical behaviors such as backward bifurcation may arise from the second one. Our results highlight the importance of validating key modeling assumptions in the development and selection of mathematical models toward practical application.

Disease dynamics in a coupled cholera model linking within-host and between-host interactions

A new modelling framework is proposed to study the within-host and between-host dynamics of cholera, a severe intestinal infection caused by the bacterium Vibrio cholerae. The within-host dynamics are characterized by the growth of highly infectious vibrios inside the human body. These vibrios shed from humans contribute to the environmental bacterial growth and the transmission of the disease among humans, providing a link from the within-host dynamics at the individual level to the between-host dynamics at the population and environmental level. A fast-slow analysis is conducted based on the two different time scales in our model. In particular, a bifurcation study is performed, and sufficient and necessary conditions are derived that lead to a backward bifurcation in cholera epidemics. Our result regarding the backward bifurcation highlights the challenges in the prevention and control of cholera.

Behavioural change models for infectious disease transmission: a systematic review (2010-2015)

We review behavioural change models (BCMs) for infectious disease transmission in humans. Following the Cochrane collaboration guidelines and the PRISMA statement, our systematic search and selection yielded 178 papers covering the period 2010-2015. We observe an increasing trend in published BCMs, frequently coupled to (re)emergence events, and propose a categorization by distinguishing how information translates into preventive actions. Behaviour is usually captured by introducing information as a dynamic parameter (76/178) or by introducing an economic objective function, either with (26/178) or without (37/178) imitation. Approaches using information thresholds (29/178) and exogenous behaviour formation (16/178) are also popular. We further classify according to disease, prevention measure, transmission model (with 81/178 population, 6/178 metapopulation and 91/178 individual-level models) and the way prevention impacts transmission. We highlight the minority (15%) of studies that use any real-life data for parametrization or validation and note that BCMs increasingly use social media data and generally incorporate multiple sources of information (16/178), multiple types of information (17/178) or both (9/178). We conclude that individual-level models are increasingly used and useful to model behaviour changes. Despite recent advancements, we remain concerned that most models are purely theoretical and lack representative data and a validation process.