Cholera Transmission Model Research Articles

Exploring noise-induced dynamics and optimal control strategy of iSIR cholera transmission model

Exploring noise-induced dynamics and optimal control strategy of iSIR cholera transmission model

Dynamical analysis of an age-structured cholera transmission model on complex networks

Cholera is a water- and food-borne infectious disease caused by the bacterium Vibrio cholerae. In this paper, we present a novel modeling framework to investigate the effect of infection age on cholera transmission in a heterogeneous population. Our model is constructed on a system with infection age on complex networks, including both direct and indirect transmission routes and demographics. The basic reproduction number R0 is derived as the spectral radius of the next generation operator, and it is verified that R0 is a sharp threshold that determines whether cholera becomes extinct or not. Numerical simulations are performed to confirm the theoretical results. Furthermore, the sensitivity analysis of the basic reproduction number to the parameters suggests that the implementation of effective drug treatment for infected individuals and the timely removal of pathogens from contaminated water are beneficial to control the spread of cholera.

Global Dynamics Analysis of a Cholera Transmission Model with General Incidence and Multiple Modes of Infection

Global Dynamics Analysis of a Cholera Transmission Model with General Incidence and Multiple Modes of Infection

Dynamics of cholera transmission model with imperfect vaccination and demographics on complex networks

Cholera is a waterborne infectious disease that continually emerges and remains an important global health burden. We formulate and investigate a cholera model with imperfect vaccination and demographics on complex networks, in which two transmission pathways, indirect environment-to-human and direct human-to-human transmissions, are incorporated simultaneously. The contacts among humans are treated as a heterogeneous network and the contacts between environment and humans as homogenous mixing. Using the spectral analysis method, the basic reproduction number is defined and verified to be a sharp threshold which completely determines global dynamical properties of model. Numerical simulations are performed to confirm the theoretical results. The results demonstrate that demographics and the degree distribution of the network are of great importance in cholera propagation, and that the degree distribution is time-dependent until the stationary state is reached. Furthermore, demographics have a significant influence on the basic reproduction number. By increasing the vaccination rate and decreasing the rate at which the vaccine wears off, cholera infection can be effectively controlled.

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.

Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine‐induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine‐induced immunity and nonlinear telegraph perturbations. First, we derive a critical value related to the basic reproduction number of the deterministic model. The key aim of this paper is to generalize the θ‐stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ‐stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under . Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.

Mathematical analysis and application of a cholera transmission model with waning vaccine-induced immunity

In this paper, a cholera infection model with vaccination is investigated, in which hyperinfectious and hypoinfectious vibrios, both human-to-human and environment-to-human transmission pathways, and waning vaccine-induced immunity are considered. The basic reproduction number is calculated and verified to be a threshold determining the global dynamics of the model. In addition, an application is demonstrated by investigating the cholera outbreak in Somalia, and the relevant control measures in the short term are given by elasticity and sensitivity analysis.

Global dynamics and optimal control of a cholera transmission model with vaccination strategy and multiple pathways.

In this paper, we consider a cholera infection model with vaccination and multiple transmission pathways. Dynamical properties of the model are analyzed in detail. It is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity; the endemic equilibrium exists and is globally asymptotically stable if the basic reproduction number is greater than unity. In addition, the model is successfully used to fit the real disease situation of cholera outbreak in Somalia. We consider an optimal control problem of cholera transmission with vaccination, quarantine, treatment and sanitation control strategies, and use Pontryagin's minimum principle to determine the optimal control level. The optimal control problem is solved numerically.

Dynamical analysis and optimal control simulation for an age-structured cholera transmission model

Cholera is an infectious disease caused by the bacterium vibrio cholerae, which can lead to widespread epidemics in the deterioration of public health systems or the associated infrastructure. Vaccination and water sanitation are two well-known methods for the prevention and intervention of cholera epidemics. In this paper, we propose an age-structured cholera model that incorporates both the environment-to-human and human-to-human transmission pathways and that includes host vaccination and water sanitation as disease control measures. We rigorously investigate the threshold dynamics of this model using the basic reproduction number derived from our analysis. Meanwhile, we perform an optimal control study to explore cost-effective intervention strategies for cholera. Our numerical simulation results show that the outcome of the optimal control is shaped by the complex interactions among the age structure of the hosts, the costs of the control measures, the transmission modes of the disease, and the different approaches of cholera intervention.

A cholera transmission model incorporating the impact of medical resources.

We propose a mathematical model for the transmission dynamics of cholera under the impact of available medical resources. The model describes the interaction between the human hosts and the pathogenic bacteria and incorporates both the environment-to-human and human-to-human transmission routes. We conduct a rigorous equilibrium analysis to the model and establish the global asymptotic stability of the disease-free equilibrium when R0 ≤ 1 and that of the endemic equilibrium when R0 > 1. As a realistic case study, we apply our model to the Yemen cholera outbreak during 2017-2018. By fitting our simulation results to the epidemic data published by the World Health Organization, we find that different levels of disease prevalence and severity are linked to different geographical regions in this country and that cholera prevention and intervention efforts should be implemented strategically with respect to these regions in Yemen.

Near real-time forecasting for cholera decision making in Haiti after Hurricane Matthew.

Computational models of cholera transmission can provide objective insights into the course of an ongoing epidemic and aid decision making on allocation of health care resources. However, models are typically designed, calibrated and interpreted post-hoc. Here, we report the efforts of a team from academia, field research and humanitarian organizations to model in near real-time the Haitian cholera outbreak after Hurricane Matthew in October 2016, to assess risk and to quantitatively estimate the efficacy of a then ongoing vaccination campaign. A rainfall-driven, spatially-explicit meta-community model of cholera transmission was coupled to a data assimilation scheme for computing short-term projections of the epidemic in near real-time. The model was used to forecast cholera incidence for the months after the passage of the hurricane (October-December 2016) and to predict the impact of a planned oral cholera vaccination campaign. Our first projection, from October 29 to December 31, predicted the highest incidence in the departments of Grande Anse and Sud, accounting for about 45% of the total cases in Haiti. The projection included a second peak in cholera incidence in early December largely driven by heavy rainfall forecasts, confirming the urgency for rapid intervention. A second projection (from November 12 to December 31) used updated rainfall forecasts to estimate that 835 cases would be averted by vaccinations in Grande Anse (90% Prediction Interval [PI] 476-1284) and 995 in Sud (90% PI 508-2043). The experience gained by this modeling effort shows that state-of-the-art computational modeling and data-assimilation methods can produce informative near real-time projections of cholera incidence. Collaboration among modelers and field epidemiologists is indispensable to gain fast access to field data and to translate model results into operational recommendations for emergency management during an outbreak. Future efforts should thus draw together multi-disciplinary teams to ensure model outputs are appropriately based, interpreted and communicated.

A model of cholera transmission with hyperinfectivity and its optimal vaccination control

The use of cholera vaccines has been increasingly recognized as an effective control measure in cholera endemic countries. Also, the disease transmissions are getting more complicated and thus comprehensive strategies to implement public health control measures are worthwhile to be investigated. In this paper, we aim to better understand the effects of HI states of vibrios from the environment and from human contacts that cause cholera outbreaks. We also present and analyze our cholera mathematical model with vaccine incorporated. Equilibrium analysis is conducted in the case with constant control for both epidemic and endemic dynamics. Optimal control theory is applied to seek cost-effective solutions of time-dependent vaccination strategies against cholera outbreaks. Our results show that using vaccination during cholera outbreaks at the very beginning of the onset can reduce the number of infections significantly.

Impact of oral cholera vaccines in cholera-endemic countries: A mathematical modeling study

BackgroundImpact evaluation of vaccination programs is necessary for making decisions to introduce oral cholera vaccines (OCVs) in cholera-endemic countries. MethodsWe analyzed data to forecast the future global burden of cholera. We developed a mathematical model of cholera transmission in three countries as examples: Nigeria, Uganda, and Indonesia. After fitting the model, we evaluated the impact of OCVs delivered in four vaccination strategies varying by target age group and frequency of vaccination over the period of 2015–2030. ResultsData suggest that the global annual incidence of cholera will increase from 3046238 in 2015 to 3787385 in 2030 with the highest burden in Asia and Africa where overall population size is large and the proportion of population with access to improved sanitation facilities is low. We estimate that OCV will reduce the cumulative incidence of cholera by half in Indonesia and >80% in Nigeria and Uganda when delivered to 1+ year olds every three years at a coverage rate of 50%, although cholera may persist through higher coverage rates (i.e., >90%). The proportion of person-to-person transmission compared to water-to-person transmission is positively correlated with higher vaccination impact in all three countries. ConclusionsPeriodic OCV vaccination every three or five years can significantly reduce the global burden of cholera although cholera may persist even with high OCV coverage. Vaccination impact will likely vary depending on local epidemiological conditions including age distribution of cases and relative contribution of different transmission routes.

Comparative effectiveness of different strategies of oral cholera vaccination in bangladesh: a modeling study.

BackgroundKilled, oral cholera vaccines have proven safe and effective, and several large-scale mass cholera vaccination efforts have demonstrated the feasibility of widespread deployment. This study uses a mathematical model of cholera transmission in Bangladesh to examine the effectiveness of potential vaccination strategies.Methods & FindingsWe developed an age-structured mathematical model of cholera transmission and calibrated it to reproduce the dynamics of cholera in Matlab, Bangladesh. We used the model to predict the effectiveness of different cholera vaccination strategies over a period of 20 years. We explored vaccination programs that targeted one of three increasingly focused age groups (the entire vaccine-eligible population of age one year and older, children of ages 1 to 14 years, or preschoolers of ages 1 to 4 years) and that could occur either as campaigns recurring every five years or as continuous ongoing vaccination efforts. Our modeling results suggest that vaccinating 70% of the population would avert 90% of cholera cases in the first year but that campaign and continuous vaccination strategies differ in effectiveness over 20 years. Maintaining 70% coverage of the population would be sufficient to prevent sustained transmission of endemic cholera in Matlab, while vaccinating periodically every five years is less effective. Selectively vaccinating children 1–14 years old would prevent the most cholera cases per vaccine administered in both campaign and continuous strategies.ConclusionsWe conclude that continuous mass vaccination would be more effective against endemic cholera than periodic campaigns. Vaccinating children averts more cases per dose than vaccinating all age groups, although vaccinating only children is unlikely to control endemic cholera in Bangladesh. Careful consideration must be made before generalizing these results to other regions.

Dynamics of a cholera transmission model with immunological threshold and natural phage control in reservoir.

Cholera remains epidemic and endemic in the world, causing thousands of deaths annually in locations lacking adequate sanitation and water infrastructure. Yet, its dynamics are still not fully understood. In this paper, we simplify and improve Jensen et al.'s model (PNAS 103:4652-4657, 2006) by incorporating a Minimum Infection Dose (MID) into the incidence term. We perform local stability analysis and provide bifurcation diagrams of the bacterial carrying capacity with or without shedding. Choosing parameters such that the endemic or epidemic equilibrium is unstable (as it is the case in reality), we observe numerically that for the bacterial carrying capacity (K) less than the MID (c), oscillating trajectories exist only in the microbial scale, whereas for K > c, they exist in both the microbial and population scales. In both cases, increasing pathogen shed rate ξ increases the amplitude of the trajectories and the period of the trajectories for those that are periodic. Our findings highlight the importance of the relationship among the shedding rates, K, MID, the maximum bacterial growth rate (r) and the features of the disease outbreak. In addition, we identified a region in the parameter space of our model that leads to chaotic behaviour. This could be used to explain the irregularity in the seasonal patterns of outbreaks amongst different countries, especially if the positive relationship between bacterial proliferation and temperature is considered.

Urban cholera transmission hotspots and their implications for reactive vaccination: evidence from Bissau city, Guinea bissau.

BackgroundUse of cholera vaccines in response to epidemics (reactive vaccination) may provide an effective supplement to traditional control measures. In Haiti, reactive vaccination was considered but, until recently, rejected in part due to limited global supply of vaccine. Using Bissau City, Guinea-Bissau as a case study, we explore neighborhood-level transmission dynamics to understand if, with limited vaccine and likely delays, reactive vaccination can significantly change the course of a cholera epidemic.Methods and FindingsWe fit a spatially explicit meta-population model of cholera transmission within Bissau City to data from 7,551 suspected cholera cases from a 2008 epidemic. We estimated the effect reactive vaccination campaigns would have had on the epidemic under different levels of vaccine coverage and campaign start dates. We compared highly focused and diffuse strategies for distributing vaccine throughout the city. We found wide variation in the efficiency of cholera transmission both within and between areas of the city. “Hotspots”, where transmission was most efficient, appear to drive the epidemic. In particular one area, Bandim, was a necessary driver of the 2008 epidemic in Bissau City. If vaccine supply were limited but could have been distributed within the first 80 days of the epidemic, targeting vaccination at Bandim would have averted the most cases both within this area and throughout the city. Regardless of the distribution strategy used, timely distribution of vaccine in response to an ongoing cholera epidemic can prevent cases and save lives.ConclusionsReactive vaccination can be a useful tool for controlling cholera epidemics, especially in urban areas like Bissau City. Particular neighborhoods may be responsible for driving a city's cholera epidemic; timely and targeted reactive vaccination at such neighborhoods may be the most effective way to prevent cholera cases both within that neighborhood and throughout the city.

Hydroclimatology of dual‐peak annual cholera incidence: Insights from a spatially explicit model

Cholera incidence in some regions of the Indian subcontinent may exhibit two annual peaks although the main environmental drivers that have been linked to the disease (e.g., sea surface temperature, zooplankton abundance, river discharge) peak once per year during the summer. An empirical hydroclimatological explanation relating cholera transmission to river flows and to the disease spatial spreading has been recently proposed. We specifically support and substantiate mechanistically such hypothesis by means of a spatially explicit model of cholera transmission. Our framework directly accounts for the role of a model river network in transporting and redistributing cholera bacteria among human communities as well as for spatial and temporal annual fluctuations of river flows. The model is forced by seasonal environmental drivers, namely river flow, temperature and chlorophyll concentration in the coastal environment, a proxy for Vibrio choleraeconcentration. Our results show that these drivers may suffice to generate dual‐peak cholera prevalence patterns for proper combinations of timescales involved in pathogen transport, hydrologic variability and disease unfolding. The model explains the possible occurrence of spatial patterns of cholera incidence characterized by a spring peak confined to coastal areas and a fall peak involving inland regions. Our modeling framework suggests insights on how environmental drivers concert the generation of complex spatiotemporal infections and proposes an explanation for the different cholera patterns (dual or single annual peaks) exhibited by regions that share similar hydroclimatological forcings.

Vaccination strategies for epidemic cholera in Haiti with implications for the developing world

In October 2010, a virulent South Asian strain of El Tor cholera began to spread in Haiti. Interventions have included treatment of cases and improved sanitation. Use of cholera vaccines would likely have further reduced morbidity and mortality, but such vaccines are in short supply and little is known about effective vaccination strategies for epidemic cholera. We use a mathematical cholera transmission model to assess different vaccination strategies. With limited vaccine quantities, concentrating vaccine in high-risk areas is always most efficient. We show that targeting one million doses of vaccine to areas with high exposure to Vibrio cholerae, enough for two doses for 5% of the population, would reduce the number of cases by 11%. The same strategy with enough vaccine for 30% of the population with modest hygienic improvement could reduce cases by 55% and save 3,320 lives. For epidemic cholera, we recommend a large mobile stockpile of enough vaccine to cover 30% of a country's population to be reactively targeted to populations at high risk of exposure.

Averting Cholera Cases and Deaths in Haiti

Cholera appeared in postearthquake Haiti in October 2010 and has spread to all provinces. To estimate the effects of specific interventions, investigators constructed a mathematical model of cholera transmission based on existing models and then calibrated it to data from the Haitian epidemic. The model included symptomatic and asymptomatic infections and excretion of Vibrio …

Quorum-regulated biofilms enhance the development of conditionally viable, environmental Vibrio cholerae

The factors that enhance the waterborne spread of bacterial epidemics and sustain the pathogens in nature are unclear. The epidemic diarrheal disease cholera caused by Vibrio cholerae spreads through water contaminated with the pathogen. However, the bacteria exist in water mostly as clumps of cells, which resist cultivation by standard techniques but revive into fully virulent form in the intestinal milieu. These conditionally viable environmental cells (CVEC), alternatively called viable but nonculturable cells, presumably play a crucial role in cholera epidemiology. However, the precise mechanism causing the transition of V. cholerae to the CVEC form and this form's significance in the biology of the pathogen are unknown. Here we show that this process involves biofilm formation that is dependent on quorum sensing, a regulatory response that is controlled by cell density. V. cholerae strains carrying mutations in genes required for quorum sensing and biofilm formation displayed altered CVEC formation in environmental water following intestinal infections. Analysis of naturally occurring V. cholerae CVEC showed that organisms that adopt this quiescent physiological state typically exist as clumps of cells that comprise a single clone closely related to isolates causing the most recent local cholera epidemic. These results support a model of cholera transmission in which in vivo-formed biofilms convert to CVEC upon the introduction of cholera stools into environmental water. Our data further suggest that a temporary loss of quorum sensing due to dilution of extracellular autoinducers confers a selective advantage to communities of V. cholerae by blocking quorum-mediated regulatory responses that would break down biofilms and thus interfere with CVEC formation.