Modeling cholera outbreaks

Prediction and control of cholera outbreak: Study case of Cameroon

This paper deals with the problem of the prediction and control of cholera outbreak using real data of Cameroon. We first develop and analyze a deterministic model with seasonality for the cholera, the novelty of which lies in the incorporation of undetected cases. We present the basic properties of the model and compute two explicit threshold parameters R ¯ 0 and R _ 0 that bound the effective reproduction number R 0 , from below and above, that is R _ 0 ≤ R 0 ≤ R ¯ 0 . We prove that cholera tends to disappear when R ¯ 0 ≤ 1 , while when R _ 0 > 1 , cholera persists uniformly within the population. After, assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown, we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in Cameroon. We use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon, and give a short-term forecasts of cholera in Cameroon until 2024. Numerical simulations show that (i) the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October, (ii) 90% of newly cholera infected cases that present the symptoms of cholera are not diagnosed and (iii) 60.36% of asymptomatic are detected at 14% and 86% of them recover naturally. The future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October 2023. An impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera outbreak. In the first year of monitoring, we observed a reduction of more than 75% of incidences and the disappearance of the peaks when no control are available in Cameroon. A second monitoring of control led to a further reduction of around 60% of incidences the following year, showing how impulse control could be an effective means of eradicating cholera.

Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions

A mathematical model that describes the dynamics of bacterium vibrio cholera within a fixed population considering intrinsic bacteria growth, therapeutic treatment, sanitation and vaccination rates is developed. The developed mathematical model is validated against real cholera data. A sensitivity analysis of some of the model parameters is also conducted. The intervention rates are found to be very important parameters in reducing the values of the basic reproduction number. The existence and stability of equilibrium solutions to the mathematical model are also carried out using analytical methods. The effect of some model parameters on the stability of equilibrium solutions, number of infected individuals, number of susceptible individuals and bacteria density is rigorously analyzed. One very important finding of this research work is that keeping the vaccination rate fixed and varying the treatment and sanitation rates provide a rapid decline of infection. The fourth order Runge-Kutta numerical scheme is implemented in MATLAB to generate the numerical solutions.

Mathematical Modeling of Endemic Cholera Transmission

Mathematical modeling can be used to project the impact of mass vaccination on cholera transmission. Here, we discuss 2 examples for which indirect protection from mass vaccination needs to be considered. In the first, we show that nonvaccinees can be protected by mass vaccination campaigns. This additional benefit of indirect protection improves the cost-effectiveness of mass vaccination. In the second, we model the use of mass vaccination to eliminate cholera. In this case, a high population level of immunity, including contributions from infection and vaccination, is required to reach the "herd immunity" threshold needed to stop transmission and achieve elimination.

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.

Short-term forecasts of the COVID-19 pandemic: a study case of Cameroon

In this paper, an Ensemble of Kalman filter (EnKf) approach is developed to estimate unmeasurable state variables and unknown parameters in a COVID-19 model. We first formulate a mathematical model for the dynamic transmission of COVID-19 that takes into account the circulation of free coronaviruses in the environment. We provide the basic properties of the model and compute the basic reproduction number R 0 that plays an important role in the outcome of the disease. After, assuming continuous measurement of newly COVID-19 reported cases, deceased and recovered individuals, the EnKf approach is used to estimate the unmeasured variables and unknown COVID-19 transmission rates using real data of the current COVID-19 pandemic in Cameroon. We present the forecasts of the current pandemic in Cameroon and explore the impact of non-pharmaceutical interventions such as mass media-based sensitization, social distancing, face-mask wearing, contact tracing and the desinfection and decontamination of infected places by using suitable products against free coronaviruses in the environment in order to reduce the spread of the disease. Through numerical simulations, we find that at that time (i)R 0 ≈ 2.9495 meaning that the disease will not die out without any control measures, (ii) the infection from COVID-19 infected cases is more important than the infection from free coronaviruses in the environment, (iii) the number of new COVID-19 cases will still increase and there is a necessity to increase timely the surveillance by using contact tracing and sensibilisation of the population to respect social distancing, face-masks wearing through awareness programs and (iv) the eradication of the pandemic is highly dependent on the control measures taken by governments.

Modelling the aqueous transport of an infectious pathogen in regional communities: application to the cholera outbreak in Haiti

A mathematical model is developed to describe the dynamics of the spread of a waterborne disease among communities located along a flowing waterway. The model is formulated as a system of reaction-diffusion-advection partial differential equations in this spatial setting. The compartments of the model consist of susceptible, infected, and recovered individuals in the communities along the waterway, together with a term representing the pathogen load in each community and a term representing the spatial concentration of pathogens flowing along the waterway. The model is applied to the cholera outbreak in Haiti in 2010.

A population model for the 2017/18 listeriosis outbreak in South Africa

We introduce a compartmental model of ordinary differential equations for the population dynamics of listeriosis, and we derive a model for analysing a listeriosis outbreak. The model explicitly accommodates neonatal infections. Similarly as is common in cholera modeling, we include a compartment to represent the reservoir of bacteria. We also include a compartment to represent the incubation phase. For the 2017/18 listeriosis outbreak that happened in South Africa, we calculate the time pattern and intensity of the force of infection, and we determine numerical values for some of the parameters in the model. The model is calibrated using South African data, together with existing data in the open literature not necessarily from South Africa. We make projections on the future outlook of the epidemiology of the disease and the possibility of eradication.

Non-vaccine strategies for cholera prevention and control: India's preparedness for the global roadmap

BACKGROUND

Recently World Health Organization's Global Task Force on Cholera Control (GTFCC) has published a global roadmap for prevention and control of cholera. We review preparedness of existing governmental non-vaccine programs and strategies for cholera prevention and control in India. We also describe strengths and gaps in the context of implementation of the global roadmap.

METHODS

We reviewed published literature on non-vaccine based strategies for prevention and control of cholera in India and analyzed strengths and weaknesses of Government of India's major anti-cholera and ante-diarrhea initiatives under Integrated Disease Surveillance Program (IDSP), National Rural Health Mission (NRHM), and other disease surveillance platforms.

RESULTS

The first strategy of the WHO global roadmap, namely, preparedness for early detection and outbreak containment, has been addressed by the IDSP. NRHM complements IDSP activities by focusing on sanitation, hygiene, nutrition, and safe drinking water. We identified the need to adopt stricter case definitions and data validation protocols. Multi-sectoral approach to prevent cholera occurrences and re-occurrences [the second suggested strategy in the global roadmap], highlights identification of hotspots and implementing strategies based on transmission dynamics. We recommend development of comprehensive models by integrating data sources beyond the national programs to eliminate cholera hotspots in India. Implementing the third proposed strategy in the global roadmap, coordinated technical support, resource mobilization, and partnerships at local and global levels, has major challenges in India due to structural issues related to health systems and health programs.

CONCLUSION

Even with a robust public health infrastructure, absence of a national cholera program might have resulted in lack of specific focus and concerted efforts for cholera prevention and control in India. A National Taskforce for Cholera Control must develop India-specific 'National Cholera Prevention and Response Road Map' with an appropriate administrative and financially viable framework for its implementation.

Modeling the Transmission of Vibrio aestuarianus in Pacific Oysters Using Experimental Infection Data

Vibrio aestuarianus is a bacterium related to mortality outbreaks in Pacific oysters, Crassostrea gigas, in France, Ireland, and Scotland since 2011. Knowledge about its transmission dynamics is still lacking, impairing guidance to prevent and control the related disease spread. Mathematical modeling is a relevant approach to better understand the determinants of a disease and predict its dynamics in imperfectly observed pathosystems. We developed here the first marine epidemiological model to estimate the key parameters of V. aestuarianus infection at a local scale in a small and closed oyster population under controlled laboratory conditions. Using a compartmental model accounting for free-living bacteria in seawater, we predicted the infection dynamics using dedicated and model-driven collected laboratory experimental transmission data. We estimated parameters and showed that waterborne transmission of V. aestuarianus is possible under experimental conditions, with a basic reproduction number R₀ of 2.88 (95% CI: 1.86; 3.35), and a generation time of 5.5 days. Our results highlighted a bacterial dose–dependent transmission of vibriosis at local scale. Global sensitivity analyses indicated that the bacteria shedding rate, the concentration of bacteria in seawater that yields a 50% chance of catching the infection, and the initial bacterial exposure dose W₀ were three critical parameters explaining most of the variation in the selected model outputs related to disease spread, i.e., R₀, the maximum prevalence, oyster survival curve, and bacteria concentration in seawater. Prevention and control should target the exposure of oysters to bacterial concentration in seawater. This combined laboratory–modeling approach enabled us to maximize the use of information obtained through experiments. The identified key epidemiological parameters should be better refined by further dedicated laboratory experiments. These results revealed the importance of multidisciplinary approaches to gain consistent insights into the marine epidemiology of oyster diseases.

The Other Side of the Coin: What Beneficial Microbes Can Teach Us about Pathogenic Potential

Koch's postulates and molecular Koch's postulates have made an indelible mark on how we study and classify microbes, particularly pathogens. However, rigid adherence to these historic postulates constrains our view of not only microbial pathogenesis but also host-microbe relationships in general. Collectively, the postulates imply that a "microbial pathogen" is a clearly identifiable organism with the exclusive capacity to elicit disease through an arsenal of pathogen-specific "virulence factors." This narrow definition has been repeatedly contradicted. Advances in DNA sequencing technologies and new experimental systems have revealed that the outcomes of host-microbe interactions are highly contextual and dynamic, especially those involving resident microbiota and variable aspects of host biology. Clarifying what differentiates pathogenic from non-pathogenic microbes, including their paradoxical ability to masquerade as one another, is critical to developing targeted diagnostics and treatments for infectious disease. Such endeavors will also inform the design of therapeutic strategies based on microbiome engineering by providing insights into how manipulating entire host-microbe systems may directly or indirectly alter the pathogenic potential of microbial communities. With these goals in mind, we discuss the need to develop experimental models that better capture the contexts that determine the nature of host-microbe relationships. To demonstrate the potential of one such model-the zebrafish and its resident microbiota-we describe recent work that has revealed the thin line between pathogenic and mutualistic relationships, how the intestine physically shapes bacterial populations and inflammation, and the ability of microbial transmission to override the host's innate immune system.

Cholera Epidemics of the Past Offer New Insights Into an Old Enemy

Background

Although cholera is considered the quintessential long-cycle waterborne disease, studies have emphasized the existence of short-cycle (food, household) transmission. We investigated singular Danish cholera epidemics (in 1853) to elucidate epidemiological parameters and modes of spread.

Methods

Using time series data from cities with different water systems, we estimated the intrinsic transmissibility (R₀). Accessing cause-specific mortality data, we studied clinical severity and age-specific impact. From physicians’ narratives we established transmission chains and estimated serial intervals.

Results

Epidemics were seeded by travelers from cholera-affected cities; initial transmission chains involving household members and caretakers ensued. Cholera killed 3.4%–8.9% of the populations, with highest mortality among seniors (16%) and lowest in children (2.7%). Transmissibility (R₀) was 1.7–2.6 and the serial interval was estimated at 3.7 days (95% confidence interval, 2.9–4.7 days). The case fatality ratio (CFR) was high (54%–68%); using R₀ we computed an adjusted CFR of 4%–5%.

Conclusions

Short-cycle transmission was likely critical to early secondary transmission in historic Danish towns. The outbreaks resembled the contemporary Haiti outbreak with respect to transmissibility, age patterns, and CFR, suggesting a role for broader hygiene/sanitation interventions to control contemporary outbreaks.

Quantifying the relative effects of environmental and direct transmission of norovirus

Norovirus is a common cause of outbreaks of acute gastroenteritis in health- and child-care settings, with serial outbreaks also frequently observed aboard cruise ships. The relative contributions of environmental and direct person-to-person transmission of norovirus have hitherto not been quantified. We employ a novel mathematical model of norovirus transmission, and fit the model to daily incidence data from a major norovirus outbreak on a cruise ship, and examine the relative efficacy of potential control strategies aimed at reducing environmental and/or direct transmission. The reproduction number for environmental and direct transmission combined is [Formula: see text] [6.1,9.5], and of environmental transmission alone is [Formula: see text] [0.9,2.6]. Direct transmission is overwhelmingly due to passenger-to-passenger contacts, but crew can act as a reservoir of infection from cruise to cruise. This is the first quantification of the relative roles of environmental and direct transmission of norovirus. While environmental transmission has the potential to maintain a sustained series of outbreaks aboard a cruise ship in the absence of strict sanitation practices, direct transmission dominates. We find that intensive promotion of good hand washing practices may prevent outbreaks. Isolation of ill passengers and cleaning are beneficial, but appear to be less efficacious at outbreak control.

The importance of thinking beyond the water-supply in cholera epidemics: A historical urban case-study

BACKGROUND

Planning interventions to respond to cholera epidemics requires an understanding of the major transmission routes. Interrupting short-cycle (household, foodborne) transmission may require different approaches as compared long-cycle (environmentally-mediated/waterborne) transmission. However, differentiating the relative contribution of short- and long-cycle routes has remained difficult, and most cholera outbreak control efforts focus on interrupting long-cycle transmission. Here we use high-resolution epidemiological and municipal infrastructure data from a cholera outbreak in 1853 Copenhagen to explore the relative contribution of short- and long-cycle transmission routes during a major urban epidemic.

METHODOLOGY/PRINCIPAL FINDINGS

We fit a spatially explicit time-series meta-population model to 6,552 physician-reported cholera cases from Copenhagen in 1853. We estimated the contribution of long-cycle waterborne transmission between neighborhoods using historical municipal water infrastructure data, fitting the force of infection from hydraulic flow, then comparing model performance. We found the epidemic was characterized by considerable transmission heterogeneity. Some neighborhoods acted as localized transmission hotspots, while other neighborhoods were less affected or important in driving the epidemic. We found little evidence to support long-cycle transmission between hydrologically-connected neighborhoods. Collectively, these findings suggest short-cycle transmission was significant.

CONCLUSIONS/SIGNIFICANCE

Spatially targeted cholera interventions, such as reactive vaccination or sanitation/hygiene campaigns in hotspot neighborhoods, would likely have been more effective in this epidemic than control measures aimed at interrupting long-cycle transmission, such as improving municipal water quality. We recommend public health planners consider programs aimed at interrupting short-cycle transmission as essential tools in the cholera control arsenal.

Transmission dynamics of cholera in Yemen, 2017: a real time forecasting

BACKGROUND

A large epidemic of cholera, caused by Vibrio cholerae, serotype Ogawa, has been ongoing in Yemen, 2017. To improve the situation awareness, the present study aimed to forecast the cholera epidemic, explicitly addressing the reporting delay and ascertainment bias.

METHODS

Using weekly incidence of suspected cases, updated as a revised epidemic curve every week, the reporting delay was explicitly incorporated into the estimation model. Using the weekly case fatality risk as calculated by the World Health Organization, ascertainment bias was adjusted, enabling us to parameterize the family of logistic curves (i.e., logistic and generalized logistic models) for describing the unbiased incidence in 2017.

RESULTS

The cumulative incidence at the end of the epidemic, was estimated at 790,778 (95% CI: 700,495, 914,442) cases and 767,029 (95% CI: 690,877, 871,671) cases, respectively, by using logistic and generalized logistic models. It was also estimated that we have just passed through the epidemic peak by week 26, 2017. From week 27 onwards, the weekly incidence was predicted to decrease.

CONCLUSIONS

Cholera epidemic in Yemen, 2017 was predicted to soon start to decrease. If the weekly incidence is reported in the up-to-the-minute manner and updated in later weeks, not a single data point but the entire epidemic curve must be precisely updated.

The African cholera surveillance network (Africhol) consortium meeting, 10-11 June 2015, Lomé, Togo

The fifth annual meeting of the African cholera surveillance network (Africhol) took place on 10–11 June 2015 in Lomé, Togo. Together with international partners, representatives from the 11 member countries -Cameroon, Côte d’Ivoire, Democratic Republic of Congo, Guinea, Kenya, Mozambique, Nigeria, Tanzania, Togo, Uganda, Zimbabwe- and an invited country (Malawi) shared their experience. The meeting featured three sessions: i) cholera surveillance, prevention and control in participating countries, ii) cholera surveillance methodology, such as cholera mapping, cost-effectiveness studies and the issue of overlapping epidemics from different diseases, iii) cholera laboratory diagnostics tools and capacity building. The meeting has greatly benefitted from the input of technical expertise from participating institutions and the observations emerging from the meeting should enable national teams to make recommendations to their respective governments on the most appropriate and effective measures to be taken for the prevention and control of cholera.

Recommendations for future activities included collecting precise burden estimates in surveillance sites; modeling cholera burden for Africa; setting up cross-border collaborations; strengthening laboratory capacity for the confirmation of suspected cholera cases and for vaccine impact assessment in settings where oral cholera vaccine would be used; adapting cholera surveillance to concurrent issues (e.g., Ebola); and developing national cholera control plans including rationale vaccination strategies together with other preventive and control measures such as improvements in water, sanitation and hygiene (WASH).

Seasonality and the effectiveness of mass vaccination

Many infectious diseases have seasonal outbreaks, which may be driven by cyclical environmental conditions (e.g., an annual rainy season) or human behavior (e.g., school calendars or seasonal migration). If a pathogen is only transmissible for a limited period of time each year, then seasonal outbreaks could infect fewer individuals than expected given the pathogen's in-season transmissibility. Influenza, with its short serial interval and long season, probably spreads throughout a population until a substantial fraction of susceptible individuals are infected. Dengue, with a long serial interval and shorter season, may be constrained by its short transmission season rather than the depletion of susceptibles. Using mathematical modeling, we show that mass vaccination is most efficient, in terms of infections prevented per vaccine administered, at high levels of coverage for pathogens that have relatively long epidemic seasons, like influenza, and at low levels of coverage for pathogens with short epidemic seasons, like dengue. Therefore, the length of a pathogen's epidemic season may need to be considered when evaluating the costs and benefits of vaccination programs.

Strategies to Prevent Cholera Introduction during International Personnel Deployments: A Computational Modeling Analysis Based on the 2010 Haiti Outbreak

BACKGROUND

Introduction of Vibrio cholerae to Haiti during the deployment of United Nations (UN) peacekeepers in 2010 resulted in one of the largest cholera epidemics of the modern era. Following the outbreak, a UN-commissioned independent panel recommended three pre-deployment intervention strategies to minimize the risk of cholera introduction in future peacekeeping operations: screening for V. cholerae carriage, administering prophylactic antimicrobial chemotherapies, or immunizing with oral cholera vaccines. However, uncertainty regarding the effectiveness of these approaches has forestalled their implementation by the UN. We assessed how the interventions would have impacted the likelihood of the Haiti cholera epidemic.

METHODS AND FINDINGS

We developed a stochastic model for cholera importation and transmission, fitted to reported cases during the first weeks of the 2010 outbreak in Haiti. Using this model, we estimated that diagnostic screening reduces the probability of cases occurring by 82% (95% credible interval: 75%, 85%); however, false-positive test outcomes may hamper this approach. Antimicrobial chemoprophylaxis at time of departure and oral cholera vaccination reduce the probability of cases by 50% (41%, 57%) and by up to 61% (58%, 63%), respectively. Chemoprophylaxis beginning 1 wk before departure confers a 91% (78%, 96%) reduction independently, and up to a 98% reduction (94%, 99%) if coupled with vaccination. These results are not sensitive to assumptions about the background cholera incidence rate in the endemic troop-sending country. Further research is needed to (1) validate the sensitivity and specificity of rapid test approaches for detecting asymptomatic carriage, (2) compare prophylactic efficacy across antimicrobial regimens, and (3) quantify the impact of oral cholera vaccine on transmission from asymptomatic carriers.

CONCLUSIONS

Screening, chemoprophylaxis, and vaccination are all effective strategies to prevent cholera introduction during large-scale personnel deployments such as that precipitating the 2010 Haiti outbreak. Antimicrobial chemoprophylaxis was estimated to provide the greatest protection at the lowest cost among the approaches recently evaluated by the UN.

Cholera transmission dynamic models for public health practitioners

Great progress has been made in mathematical models of cholera transmission dynamics in recent years. However, little impact, if any, has been made by models upon public health decision-making and day-to-day routine of epidemiologists. This paper provides a brief introduction to the basics of ordinary differential equation models of cholera transmission dynamics. We discuss a basic model adapted from Codeço (2001), and how it can be modified to incorporate different hypotheses, including the importance of asymptomatic or inapparent infections, and hyperinfectious V. cholerae and human-to-human transmission. We highlight three important challenges of cholera models: (1) model misspecification and parameter uncertainty, (2) modeling the impact of water, sanitation and hygiene interventions and (3) model structure. We use published models, especially those related to the 2010 Haitian outbreak as examples. We emphasize that the choice of models should be dictated by the research questions in mind. More collaboration is needed between policy-makers, epidemiologists and modelers in public health.

Methods to assess the impact of mass oral cholera vaccination campaigns under real field conditions

There is increasing interest to use oral cholera vaccination as an additional strategy to water and sanitation interventions against endemic and epidemic cholera. There are two internationally-available and WHO-prequalified oral cholera vaccines: an inactivated vaccine containing killed whole-cells of V. cholerae O1 with recombinant cholera toxin B-subunit (WC/rBS) and a bivalent inactivated vaccine containing killed whole cells of V. cholerae O1 and V. cholerae O139 (BivWC). The efficacy, effectiveness, direct and indirect (herd) protection conferred by WC/rBS and BivWC are well established. Yet governments may need local evidence of vaccine impact to justify and scale-up mass oral cholera vaccination campaigns. We discuss various approaches to assess oral cholera vaccine protection, which may be useful to policymakers and public health workers considering deployment and evaluation of the vaccine.

Modeling the effect of water, sanitation, and hygiene and oral cholera vaccine implementation in Haiti

In 2010, toxigenic Vibrio cholerae was newly introduced to Haiti. Because resources are limited, decision-makers need to understand the effect of different preventive interventions. We built a static model to estimate the potential number of cholera cases averted through improvements in coverage in water, sanitation and hygiene (WASH) (i.e., latrines, point-of-use chlorination, and piped water), oral cholera vaccine (OCV), or a combination of both. We allowed indirect effects and non-linear relationships between effect and population coverage. Because there are limited incidence data for endemic cholera in Haiti, we estimated the incidence of cholera over 20 years in Haiti by using data from Malawi. Over the next two decades, scalable WASH interventions could avert 57,949-78,567 cholera cases, OCV could avert 38,569-77,636 cases, and interventions that combined WASH and OCV could avert 71,586-88,974 cases. Rate of implementation is the most influential variable, and combined approaches maximized the effect.