Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir

Global prevalence patterns and distribution of Vibrio cholerae: A systematic review and meta-analysis of 176,740 samples

This global systematic review and meta-analysis of Vibrio cholerae prevalence, covering environmental, food, animal, and human samples, analysed 111 studies from five databases. The meta-analysis, adhering to standard reporting guidelines, revealed a pooled prevalence of 10.6 % (95 % CI; 8.2 - 13.5; I2 = 99.595 %, p < 0.001) from 176,740 samples, including 27,219 cholera cases. Despite significant publication bias (Egger's test, p = 0.00018), prevalence estimate remained stable in leave-one-out analysis. Subgroup analysis showed prevalence varied by region, with Indonesia highest (55.2 %) and Jordan lowest (0.2 %). Asia continent had the highest prevalence (13.9 %), followed by South America (12.1 %), and lowest in Europe (3.8 %). Environmental samples exhibited the highest prevalence (24.9 %), while human samples had the lowest (7.1 %). The pervasive presence of V. cholerae in environmental resources highlights the persistent risk of global cholera outbreaks, necessitating urgent proactive measures and ongoing surveillance for effective cholera control.

Impact of a multi-pronged cholera intervention in an endemic setting

Cholera is a bacterial water-borne diarrheal disease transmitted via the fecal-oral route that causes high morbidity in sub-Saharan Africa and Asia. It is preventable with vaccination, and Water, Sanitation, and Hygiene (WASH) improvements. However, the impact of vaccination in endemic settings remains unclear. Cholera is endemic in the city of Kalemie, on the shore of Lake Tanganyika, in the Democratic Republic of Congo, where both seasonal mobility and the lake, a potential environmental reservoir, may promote transmission. Kalemie received a vaccination campaign and WASH improvements in 2013-2016. We assessed the impact of this intervention to inform future control strategies in endemic settings. We fit compartmental models considering seasonal mobility and environmentally-based transmission. We estimated the number of cases the intervention avoided, and the relative contributions of the elements promoting local cholera transmission. We estimated the intervention avoided 5,259 cases (95% credible interval: 1,576.6-11,337.8) over 118 weeks. Transmission did not rely on seasonal mobility and was primarily environmentally-driven. Removing environmental exposure or contamination could control local transmission. Repeated environmental exposure could maintain high population immunity and decrease the impact of vaccination in similar endemic areas. Addressing environmental exposure and contamination should be the primary target of interventions in such settings.

Multiple endemic equilibria in an environmentally-transmitted disease with three disease stages

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R∗>1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R∗<1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R∗ appearing in this model are both responsible for the existence of endemic states.

Participatory Disease Surveillance for the Early Detection of Cholera-Like Diarrheal Disease Outbreaks in Rural Villages in Malawi: Prospective Cohort Study

BACKGROUND

Cholera-like diarrheal disease (CLDD) outbreaks are complex and influenced by environmental factors, socioeconomic conditions, and population dynamics, leading to limitations in traditional surveillance methods. In Malawi, cholera is considered an endemic disease. Its epidemiological profile is characterized by seasonal patterns, often coinciding with the rainy season when contamination of water sources is more likely. However, the outbreak that began in March 2022 has extended to the dry season, with deaths reported in all 29 districts. It is considered the worst outbreak in the past 10 years.

OBJECTIVE

This study aims to evaluate the feasibility and outcomes of participatory surveillance (PS) using interactive voice response (IVR) technology for the early detection of CLDD outbreaks in Malawi.

METHODS

This longitudinal cohort study followed 740 households in rural settings in Malawi for 24 weeks. The survey tool was designed to have 10 symptom questions collected every week. The proxies' rationale was related to exanthematic, ictero-hemorragica for endemic diseases or events, diarrhea and respiratory/targeting acute diseases or events, and diarrhea and respiratory/targeting seasonal diseases or events. This work will focus only on the CLDD as a proxy for gastroenteritis and cholera. In this study, CLDD was defined as cases where reports indicated diarrhea combined with either fever or vomiting/nausea.

RESULTS

During the study period, our data comprised 16,280 observations, with an average weekly participation rate of 35%. Maganga TA had the highest average of completed calls, at 144.83 (SD 10.587), while Ndindi TA had an average of 123.66 (SD 13.176) completed calls. Our findings demonstrate that this method might be effective in identifying CLDD with a notable and consistent signal captured over time (R2=0.681404). Participation rates were slightly higher at the beginning of the study and decreased over time, thanks to the sensitization activities rolled out at the CBCCs level. In terms of the attack rates for CLDD, we observed similar rates between Maganga TA and Ndindi TA, at 16% and 15%, respectively.

CONCLUSIONS

PS has proven to be valuable for the early detection of epidemics. IVR technology is a promising approach for disease surveillance in rural villages in Africa, where access to health care and traditional disease surveillance methods may be limited. This study highlights the feasibility and potential of IVR technology for the timely and comprehensive reporting of disease incidence, symptoms, and behaviors in resource-limited settings.

Prevention and control of Ebola virus transmission: mathematical modelling and data fitting

The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled.

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.

Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as " R 0 ", to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana-Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.

Wildlife vaccination strategies for eliminating bovine tuberculosis in white-tailed deer populations

Many pathogens of humans and livestock also infect wildlife that can act as a reservoir and challenge disease control or elimination. Efficient and effective prioritization of research and management actions requires an understanding of the potential for new tools to improve elimination probability with feasible deployment strategies that can be implemented at scale. Wildlife vaccination is gaining interest as a tool for managing several wildlife diseases. To evaluate the effect of vaccinating white-tailed deer (Odocoileus virginianus), in combination with harvest, in reducing and eliminating bovine tuberculosis from deer populations in Michigan, we developed a mechanistic age-structured disease transmission model for bovine tuberculosis with integrated disease management. We evaluated the impact of pulse vaccination across a range of vaccine properties. Pulse vaccination was effective for reducing disease prevalence rapidly with even low (30%) to moderate (60%) vaccine coverage of the susceptible and exposed deer population and was further improved when combined with increased harvest. The impact of increased harvest depended on the relative strength of transmission modes, i.e., direct vs indirect transmission. Vaccine coverage and efficacy were the most important vaccine properties for reducing and eliminating disease from the local population. By fitting the model to the core endemic area of bovine tuberculosis in Michigan, USA, we identified feasible integrated management strategies involving vaccination and increased harvest that reduced disease prevalence in free-ranging deer. Few scenarios led to disease elimination due to the chronic nature of bovine tuberculosis. A long-term commitment to regular vaccination campaigns, and further research on increasing vaccines efficacy and uptake rate in free-ranging deer are important for disease management.

Anticipatory decision-making for cholera in Malawi

Climate change raises an old disease to a new level of public health threat. The causative agent, Vibrio cholerae, native to aquatic ecosystems, is influenced by climate and weather processes. The risk of cholera is elevated in vulnerable populations lacking access to safe water and sanitation infrastructure. Predictive intelligence, employing mathematical algorithms that integrate earth observations and heuristics derived from microbiological, sociological, and weather data, can provide anticipatory decision-making capabilities to reduce the burden of cholera and save human lives. An example offered here is the recent outbreak of cholera in Malawi, predicted in advance by such algorithms.

Edge-based compartmental modeling for the spread of cholera on random networks: A case study in Somalia

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.

Effect of cross-immunity in a two-strain cholera model with aquatic component

The bacteria Vibrio cholerae relies heavily upon an aquatic reservoir as a transmission route with two distinct serotypes observed in many recent outbreaks. In this paper, we extend previously studied ordinary differential equation epidemiological models to create a two-strain SIRP (susceptible-infectious-recovered-pathogen) system which incorporates both partial cross-immunity between disease strains and environmental pathogen transmission. Of particular interest are undamped anti-phase periodic solutions, as these display a type of coexistence where strains routinely switch dominance, and understanding what drives this switch can optimize the efficiency of the host population's control measures against the disease. We derive the basic reproduction number R0 and use stability analysis to examine the disease free and single-strain equilibria. We formulate a unique coexistence equilibrium and prove uniform persistence of both strains when R0>1. In addition, we simulate solutions to this system, along with seasonally forced versions of the model with and without host coinfection. Cross-immunity and transmission pathways influence damped or sustained oscillatory dynamics, where the presence of seasonality can modify, amplify or synchronize the period and phase of serotypes, driving epidemic waves. Cycling of serotypes over large time intervals, similar to observed data, is found for a range of cross-immunity levels, and the inclusion of coinfection in the model contributes to sustained anti-phase periodic solutions.

Rich dynamics of a bidirectionally linked immuno-epidemiological model for cholera

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.

Relating quanta conservation and compartmental epidemiological models of airborne disease outbreaks in buildings

We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition.

Combining a parsimonious mathematical model with infection data from tailor-made experiments to understand environmental transmission

Although most infections are transmitted through the environment, the processes underlying the environmental stage of transmission are still poorly understood for most systems. Improved understanding of the environmental transmission dynamics is important for effective non-pharmaceutical intervention strategies. To study the mechanisms underlying environmental transmission we formulated a parsimonious modelling framework including hypothesised mechanisms of pathogen dispersion and decay. To calibrate and validate the model, we conducted a series of experiments studying distance-dependent transmission of Campylobacter jejuni in broilers. We obtained informative simultaneous estimates for all three model parameters: the parameter of C. jejuni inactivation, the diffusion coefficient describing pathogen dispersion, and the transmission rate parameter. The time and distance dependence of transmission in the fitted model is quantitatively consistent with marked spatiotemporal patterns in the experimental observations. These results, for C. jejuni in broilers, show that the application of our modelling framework to suitable transmission data can provide mechanistic insight in environmental pathogen transmission.

Model-Based Estimation of Expected Time to Cholera Extinction in Lusaka, Zambia

The developing world has been facing a significant health issue due to cholera as an endemic communicable disease. Lusaka was Zambia's worst affected province, with 5414 reported cases of cholera during the outbreak from late October 2017 to May 12, 2018. To explore the epidemiological characteristics associated with the outbreak, we fitted weekly reported cholera cases with a compartmental disease model that incorporates two transmission routes, namely environment-to-human and human-to-human. Estimates of the basic reproduction number show that both transmission modes contributed almost equally during the first wave. In contrast, the environment-to-human transmission appears to be mostly dominating factor for the second wave. Our study finds that a massive abundance of environmental vibrio's with a huge reduction in water sanitation efficacy triggered the secondary wave. To estimate the expected time to extinction (ETE) of cholera, we formulate the stochastic version of our model and find that cholera can last up to 6.5-7 years in Lusaka if any further outbreak occurs at a later time. Results indicate that a considerable amount of attention is to be paid to sanitation and vaccination programs in order to reduce the severity of the disease and to eradicate cholera from the community in Lusaka.

Analysis of an environmental epidemic model based on voluntary vaccination policy

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.

Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries

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.

A Well-Posed Fractional Order Cholera Model with Saturated Incidence Rate

A fractional-order cholera model in the Caputo sense is constructed. The model is an extension of the Susceptible-Infected-Recovered (SIR) epidemic model. The transmission dynamics of the disease are studied by incorporating the saturated incidence rate into the model. This is particularly important since assuming that the increase in incidence for a large number of infected individualsis equivalent to a small number of infected individualsdoes not make much sense. The positivity, boundedness, existence, and uniqueness of the solution of the model are also studied. Equilibrium solutions are computed, and their stability analyses are shown to depend on a threshold quantity, the basic reproduction ratio (R0). It is clearly shown that if R0<1, the disease-free equilibrium is locally asymptotically stable, whereas if R0>1, the endemic equilibrium exists and is locally asymptotically stable. Numerical simulations are carried out to support the analytic results and to show the significance of the fractional order from the biological point of view. Furthermore, the significance of awareness is studied in the numerical section.

Extensions of mean-field approximations for environmentally-transmitted pathogen networks

Many pathogens spread via environmental transmission, without requiring host-to-host direct contact. While models for environmental transmission exist, many are simply constructed intuitively with structures analogous to standard models for direct transmission. As model insights are generally sensitive to the underlying model assumptions, it is important that we are able understand the details and consequences of these assumptions. We construct a simple network model for an environmentally-transmitted pathogen and rigorously derive systems of ordinary differential equations (ODEs) based on different assumptions. We explore two key assumptions, namely homogeneity and independence, and demonstrate that relaxing these assumptions can lead to more accurate ODE approximations. We compare these ODE models to a stochastic implementation of the network model over a variety of parameters and network structures, demonstrating that with fewer restrictive assumptions we are able to achieve higher accuracy in our approximations and highlighting more precisely the errors produced by each assumption. We show that less restrictive assumptions lead to more complicated systems of ODEs and the potential for unstable solutions. Due to the rigour of our derivation, we are able to identify the reason behind these errors and propose potential resolutions.

A hospital demand and capacity intervention approach for COVID-19

The mathematical interpretation of interventions for the mitigation of epidemics in the literature often involves finding the optimal time to initiate an intervention and/or the use of the number of infections to manage impact. Whilst these methods may work in theory, in order to implement effectively they may require information which is not likely to be available in the midst of an epidemic, or they may require impeccable data about infection levels in the community. In reality, testing and cases data can only be as good as the policy of implementation and the compliance of the individuals, which implies that accurately estimating the levels of infections becomes difficult or complicated from the data that is provided. In this paper, we demonstrate a different approach to the mathematical modelling of interventions, not based on optimality or cases, but based on demand and capacity of hospitals who have to deal with the epidemic on a day to day basis. In particular, we use data-driven modelling to calibrate a susceptible-exposed-infectious-recovered-died type model to infer parameters that depict the dynamics of the epidemic in several regions of the UK. We use the calibrated parameters for forecasting scenarios and understand, given a maximum capacity of hospital healthcare services, how the timing of interventions, severity of interventions, and conditions for the releasing of interventions affect the overall epidemic-picture. We provide an optimisation method to capture when, in terms of healthcare demand, an intervention should be put into place given a maximum capacity on the service. By using an equivalent agent-based approach, we demonstrate uncertainty quantification on the likelihood that capacity is not breached, by how much if it does, and the limit on demand that almost guarantees capacity is not breached.

A fractional SVIR-B epidemic model for Cholera with imperfect vaccination and saturated treatment

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.

Dynamic analysis and optimal control of a class of SISP respiratory diseases

In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM2.5 is taken into account. The concentration response function of PM2.5 is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission P0 of PM2.5 and PM2.5 pathogenic threshold K. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate β and the inhalation rate η has the largest positive correlation. The cure rate γ of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM2.5 by reducing the PM2.5 emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients.

Bacteria-bacteriophage cycles facilitate Cholera outbreak cycles: an indirect Susceptible-Infected-Recovered-Bacteria- Phage (iSIRBP) model-based mathematical study

Cholera is an acute enteric infectious disease caused by the Gram-negative bacterium Vibrio cholerae. Despite a huge body of research, the precise nature of its transmission dynamics has yet to be fully elucidated. Mathematical models can be useful to better understand how an infectious agent can spread and be properly controlled. We develop a compartmental model describing a human population, a bacterial population as well as a phage population. We show that there might be eight equilibrium points, one of which is a disease free equilibrium point. We carry out numerical simulations and sensitivity analyses and we show that the presence of phage can reduce the number of infectious individuals. Moreover, we discuss the main implications in terms of public health management and control strategies.

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.

Vibrio cholerae O1 El Tor strains linked to global cholera show region-specific patterns by pulsed-field gel electrophoresis

Vibrio cholerae O1 El Tor, causative agent of the ongoing seventh cholera pandemic, is native to the aquatic environment of the Ganges Delta, Bay of Bengal (GDBB). Recent studies traced pandemic strains to the GDBB and proposed global spread of cholera had occurred via intercontinental transmission. In the research presented here, NotI-digested genomic DNA extracted from V. cholerae O1 clinical and environmental strains isolated in Bangladesh during 20042014 was analyzed by pulsed-field gel electrophoresis (PFGE). Results of cluster analysis showed 94.67% of the V. cholerae strains belonged to clade A and included the majority of clinical strains of spatio-temporal origin and representing different cholera endemic foci. The rest of the strains were estuarine, all environmental strains from Mathbaria, Bangladesh, and occurred as singletons, clustered in clades B and C, or in the small clades D and E. Cluster analysis of the Bangladeshi strains and including 157 El Tor strains from thirteen countries in Asia, Africa, and the Americas revealed 85% of the total set of strains belonged to clade A, indicating all were related, yet did not form an homogeneous cluster. Overall, 15% of the global strains comprised multiple small clades or segregated as singletons. Three sub-clades could be discerned within the major clade A, reflecting distinct lineages of V. cholerae O1 El Tor associated with cholera in Asia, Africa, and the Americas. The presence in Asia and the Americas of non-pandemic V. cholerae O1 El Tor populations differing by PFGE and from strains associated with cholera globally suggests different ecotypes are resident in distant geographies.

Predictive Intelligence for Cholera in Ukraine?

Cholera, an ancient waterborne diarrheal disease, remains a threat to public health, especially when climate/weather processes, microbiological parameters, and sociological determinants intersect with population vulnerabilities of loss of access to safe drinking water and sanitation infrastructure. The ongoing war in Ukraine has either damaged or severely crippled civil infrastructure, following which the human population is at risk of health disasters. This editorial highlights a perspective on using predictive intelligence to combat potential (and perhaps impending) cholera outbreaks in various regions of Ukraine. Reliable and judicious use of existing earth observations inspired mathematical algorithms integrating heuristic understanding of microbiological, sociological, and weather parameters have the potential to save or reduce the disease burden.

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.

The backward bifurcation of an age-structured cholera transmission model with saturation incidence

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.

Modeling the effect of time delay in the increment of number of hospital beds to control an infectious disease

One of the key factors to control the spread of any infectious disease is the health care facilities, especially the number of hospital beds. To assess the impact of number of hospital beds and control of an emerged infectious disease, we have formulated a mathematical model by considering population (susceptible, infected, hospitalized) and newly created hospital beds as dynamic variables. In formulating the model, we have assumed that the number of hospital beds increases proportionally to the number of infected individuals. It is shown that on a slight change in parameter values, the model enters to different kinds of bifurcations, e.g., saddle-node, transcritical (backward and forward), and Hopf bifurcation. Also, the explicit conditions for these bifurcations are obtained. We have also shown the occurrence of Bogdanov-Takens (BT) bifurcation using the Normal form. To set up a new hospital bed takes time, and so we have also analyzed our proposed model by incorporating time delay in the increment of newly created hospital beds. It is observed that the incorporation of time delay destabilizes the system, and multiple stability switches arise through Hopf-bifurcation. To validate the results of the analytical analysis, we have carried out some numerical simulations.

Fractional optimal control of compartmental SIR model of COVID-19: Showing the impact of effective vaccination

In this work a compartmental SIR model has been proposed for describing the dynamics of COVID-19 with Caputo's fractional derivative(FD). SIR compartmental model has been used here with fractional differential equations(FDEs). The mathematical model of the pandemic consists of three compartments namely susceptible, infected and recovered individuals. The dynamics of the pandemic COVID-19 with FDEs for showing the effect of memory as most of the cell biological systems can be described accurately by FDEs Time dependent control(Effective vaccination) has been applied model to formulated fractional optimal control problem(FOCP) to reduce the viral load. Pontryagin's Maximum Principle(PMP) has been used to formulate FOCP. An effective vaccination is very helpful for controlling the pandemic, which is observed through the numerical simulation via Grunwald-Letnikov(G-L) approximation. All numerical simulation work has been carried in MATLAB platform.

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.

Stability Analysis and Optimal Control of a Fractional Cholera Epidemic Model

In this paper, a fractional model for the transmission dynamics of cholera was developed. In invariant regions of the model, solutions were generated. Disease-free and endemic equilibrium points were obtained. The basic reproduction number was evaluated, and the sensitivity analysis was performed. Under the support of Pontryagin’s maximum principle, the fractional order optimal control was obtained. Furthermore, an optimal strategy was discussed, which minimized the total number of infected individuals and the costs associated with control. Treatment, vaccination, and awareness programs were regarded as three means to reduce the number of infected. Finally, numerical simulations and cost-effectiveness analysis were presented to show the result that the best strategy was the combination of treatment and awareness programs.

Epidemicity of cholera spread and the fate of infection control measures

The fate of ongoing infectious disease outbreaks is predicted through reproduction numbers, defining the long-term establishment of the infection, and epidemicity indices, tackling the reactivity of the infectious pool to new contagions. Prognostic metrics of unfolding outbreaks are of particular importance when designing adaptive emergency interventions facing real-time assimilation of epidemiological evidence. Our aim here is twofold. First, we propose a novel form of the epidemicity index for the characterization of cholera epidemics in spatial models of disease spread. Second, we examine in hindsight the survey of infections, treatments and containment measures carried out for the now extinct 2010–2019 Haiti cholera outbreak, to suggest that magnitude and timing of non-pharmaceutical and vaccination interventions imply epidemiological responses recapped by the evolution of epidemicity indices. Achieving negative epidemicity greatly accelerates fading of infections and thus proves a worthwhile target of containment measures. We also show that, in our model, effective reproduction numbers and epidemicity indices are explicitly related. Therefore, providing an upper bound to the effective reproduction number (significantly lower than the unit threshold) warrants negative epidemicity and, in turn, a rapidly fading outbreak preventing coalescence of sparse local sub-threshold flare-ups.

Vaccine efficacy and SARS-CoV-2 control in California and U.S. during the session 2020-2026: A modeling study

BACKGROUND

Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates, the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic.

METHODS

We simulated a five compartment mathematical model to analyze the pandemic scenario in both California, and whole U.S. We considered four vaccines, Pfizer (95%), Moderna (94%), AstraZeneca (79%), and Johnson & Johnson (72%), which are being used rigorously to control the SARS-CoV-2 pandemic, in addition with two special cases: a vaccine with 100% efficacy rate and no vaccine under use. SARS-CoV-2 related data of California, and U.S. were used in this study.

FINDINGS

Both the infection and death rates are very high in California. Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer vaccine. During this time, six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697% and 98.30%, respectively. However, according to the considered model, this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used. On the other hand, the daily cases and deaths in the U.S. will be under control at the end of 2026 with multiple waves. Although the number of susceptible people will fall down to none in the beginning of 2027, there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100% effective vaccine or Pfizer, and at that case vaccination program must run till the mid of 2028. According to this study, the unconfirmed-infectious and infected cases will be under control at the end of 2027 and at the mid of 2028, respectively.

INTERPRETATION

The more effective a vaccine is, the less people suffer from this malign infection. Vaccines which are less than 90% effective do not have notable contribution to control the pandemic besides hard immunity. Furthermore, specific groups of people are getting prioritized initially, mass vaccination and quick responses are required to control the spread of this disease.

Threat, challenges, and preparedness for future pandemics: A descriptive review of phylogenetic analysis based predictions

For centuries the world has been confronted with many infectious diseases, with a potential to turn into a pandemic posing a constant threat to human lives. Some of these pandemics occurred due to the emergence of new disease or re-emergence of previously known diseases with a few mutations. In such scenarios their optimal prevention and control options were not adequately developed. Most of these diseases are highly contagious and for their timely control, knowledge about the pathogens and disease progression is the basic necessity. In this review, we have presented a documented chronology of the earlier pandemics, evolutionary analysis of the infectious disease with pandemic potential, the role of RNA, difficulties in controlling pandemics, and the likely pathogens that could trigger future pandemics. In this study, the evolutionary history of the pathogens was identified by carrying out phylogenetic analysis. The percentage similarity between different infectious diseases is critically analysed for the identification of their correlation using online sequence matcher tools. The Baltimore classification system was used for finding the genomic nature of the viruses. It was observed that most of the infectious pathogens rise from their animal hosts with some mutations in their genome composition. The phylogenetic tree shows that the single-stranded RNA diseases have a common origin and many of them are having high similarity percentage. The outcomes of this study will help in the identification of potential pathogens that can cause future pandemics. This information will be helpful in the development of early detection techniques, devising preventive mechanism to limit their spread, prophylactic measures, Infection control and therapeutic options, thereby, strengthening our approach towards global preparedness against future pandemics.

Drought-related cholera outbreaks in Africa and the implications for climate change: a narrative review

Africa has historically seen several periods of prolonged and extreme droughts across the continent, causing food insecurity, exacerbating social inequity and frequent mortality. A known consequence of droughts and their associated risk factors are infectious disease outbreaks, which are worsened by malnutrition, poor access to water, sanitation and hygiene and population displacement. Cholera is a potential causative agent of such outbreaks. Africa has the highest global cholera burden, several drought-prone regions and high levels of inequity. Despite this, research on cholera and drought in Africa is lacking. Here, we review available research on drought-related cholera outbreaks in Africa and identify a variety of potential mechanisms through which these outbreaks occurred, including poor access to water, marginalization of refugees and nomadic populations, expansion of informal urban settlements and demographic risks. Future climate change may alter precipitation, temperature and drought patterns, resulting in more extremes, although these changes are likely to be spatially heterogeneous. Despite high uncertainty in future drought projections, increases in drought frequency and/or durations have the potential to alter these related outbreaks into the future, potentially increasing cholera burden in the absence of countermeasures (e.g. improved sanitation infrastructure). To enable effective planning for a potentially more drought-prone Africa, inequity must be addressed, research on the health implications of drought should be enhanced, and better drought diplomacy is required to improve drought resilience under climate change.

Caputo fractional-order SEIRP model for COVID-19 Pandemic

We propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19 pandemic. The newly proposed nonlinear fractional order model is an extension of a recently formulated integer-order COVID-19 mathematical model. Using basic concepts such as continuity and Banach fixed-point theorem, existence and uniqueness of the solution to the proposed model were shown. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers and generalized Ulam-Hyers stability criteria. The concept of next-generation matrix was used to compute the basic reproduction number R0, a number that determines the spread or otherwise of the disease into the general population. We also investigated the local asymptotic stability for the derived disease-free equilibrium point. Numerical simulation of the constructed epidemic model was carried out using the fractional Adam-Bashforth-Moulton method to validate the obtained theoretical results.

Fractional-Order Modelling and Optimal Control of Cholera Transmission

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

Exploring relationships between drought and epidemic cholera in Africa using generalised linear models

Background

Temperature and precipitation are known to affect Vibrio cholerae outbreaks. Despite this, the impact of drought on outbreaks has been largely understudied. Africa is both drought and cholera prone and more research is needed in Africa to understand cholera dynamics in relation to drought.

Methods

Here, we analyse a range of environmental and socioeconomic covariates and fit generalised linear models to publicly available national data, to test for associations with several indices of drought and make cholera outbreak projections to 2070 under three scenarios of global change, reflecting varying trajectories of CO₂ emissions, socio-economic development, and population growth.

Results

The best-fit model implies that drought is a significant risk factor for African cholera outbreaks, alongside positive effects of population, temperature and poverty and a negative effect of freshwater withdrawal. The projections show that following stringent emissions pathways and expanding sustainable development may reduce cholera outbreak occurrence in Africa, although these changes were spatially heterogeneous.

Conclusions

Despite an effect of drought in explaining recent cholera outbreaks, future projections highlighted the potential for sustainable development gains to offset drought-related impacts on cholera risk. Future work should build on this research investigating the impacts of drought on cholera on a finer spatial scale and potential non-linear relationships, especially in high-burden countries which saw little cholera change in the scenario analysis.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-021-06856-4.

Mathematical modeling of the influence of cultural practices on cholera infections in Cameroon

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), R_c, 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.

Threshold dynamics of a nonlocal and delayed cholera model in a spatially heterogeneous environment

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.

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.

Modeling the Effectiveness of TV and Social Media Advertisements on the Dynamics of Water-Borne Diseases

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.

A dose response model for Staphylococcus aureus

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.

Optimizing the early detection of low pathogenic avian influenza H7N9 virus in live bird markets

In Southeast Asia, surveillance at live bird markets (LBMs) has been identified as crucial for detecting avian influenza viruses (AIV) and reducing the risk of human infections. However, the design of effective surveillance systems in LBMs remains complex given the rapid turn-over of poultry. We developed a deterministic transmission model to provide guidance for optimizing AIV surveillance efforts. The model was calibrated to fit one of the largest LBMs in northern Vietnam at high risk of low pathogenic H7N9 virus introduction from China to identify the surveillance strategy that optimizes H7N9 detection. Results show that (i) using a portable diagnostic device would slightly reduce the number of infected birds leaving the LBM before the first detection, as compared to a laboratory-based diagnostic strategy, (ii) H7N9 detection could become more timely by sampling birds staying overnight, just before new susceptible birds are introduced at the beginning of a working day, and (iii) banning birds staying overnight would represent an effective intervention to reduce the risk of H7N9 spread but would decrease the likelihood of virus detection if introduced. These strategies should receive high priority in Vietnam and other Asian countries at risk of H7N9 introduction.

Optimal Control Analysis of Cholera Dynamics in the Presence of Asymptotic Transmission

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.

Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics

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.

A mathematical model for Vibrio-phage interactions

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.

An analysis of compounding factors of epidemics in complex emergencies: a system dynamics approach

Purpose

This study aims to describe the compounding factors in a complex emergency, which exacerbate a cholera epidemic among vulnerable populations due to supply chain disruptions. Basic needs such as food, medicine, water, sanitation and hygiene commodities are critical to reduce the incidence rate of cholera and control the spread of infection. Conflicts cause damage to infrastructure, displace vulnerable populations and restrict the flow of goods from both commercial and humanitarian organizations. This study assesses the underlying internal and external factors that either aggravate or mitigate the risk of a cholera outbreak in such settings, using Yemen as a case study.

Design/methodology/approach

This study adopts a system dynamics methodology to analyze factors that influence cholera outbreaks in the context of the Yemeni Civil War. A causal loop diagram with multiple components was constructed to represent the complexities of humanitarian situations that require critical decision-making. The model was built using data from humanitarian organizations, non-governmental organizations and practitioners, along with literature from academic sources. Variables in the model were confirmed through semi-structured interviews with a field expert.

Findings

Compounding factors that influenced the cholera outbreak in Yemen are visualized in a causal loop diagram, which can improve the understanding of relationships where numerous uncertainties exist. A strong link exists between humanitarian response and the level of infrastructure development in a country. Supply chains are affected by constraints deriving from the Yemeni conflict, further inhibiting the use of infrastructure, which limits access to basic goods and services. Aligning long-term development objectives with short-term humanitarian response efforts can create more flexible modes of assistance to prevent and control future outbreaks.

Research limitations/implications

The model focuses on the qualitative aspects of system dynamics to visualize the logistics and supply chain-related constraints that impact cholera prevention, treatment and control through humanitarian interventions. The resulting causal loop diagram is bounded by the Yemen context; thus, an extension of the model adapted for other contexts is recommended for further study.

Practical implications

This study presents a systematic view of dynamic factors existing in complex emergencies that have cause-and-effect relationships. Several models of cholera outbreaks have been used in previous studies, primarily focusing on the modes and mechanisms of transmission throughout a population. However, such models typically do not include other internal and external factors that influence the population and context at the site of an outbreak. This model incorporates those factors from a logistics perspective to address the distribution of in-kind goods and cash and voucher assistance.

Social implications

This study has been aligned with six of the United Nations Sustainable Development Goals (SDGs), using their associated targets in the model as variables that influence the cholera incidence rate. Recognizing that the SDGs are interlinked, as are the dynamic factors in complex humanitarian emergencies, the authors have chosen to take an interdisciplinary approach to consider social, economic and environmental factors that may be impacted by this research.

Originality/value

This paper provides an insight into the underlying inter-relations of internal and external factors present in the context of a cholera outbreak in a complex crisis. Supply chains for food; water, sanitation and hygiene; and health products are crucial to help prevent, control and treat an outbreak. The model exposes vulnerabilities in the supply chain, which may offer guidance for decision makers to improve resilience, reduce disruptions and decrease the severity of cholera outbreaks.

DYNAMICS OF CHOLERA EPIDEMIC MODELS IN FLUCTUATING ENVIRONMENTS

Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction valueR s is defined in terms of the basic reproduction number R 0 for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. WhenR s < 1 , the cholera infection will extinct within finite periods of time almost surely. WhenR s > 1 , the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number R 0 for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such thatR s < 1 , the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out.