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.

Household Disinfection Interventions to Prevent Cholera Transmission: Facilitators, Barriers, Training, and Evidence Needs.

There are two common household disinfection interventions to prevent interhousehold transmission of cholera: household spraying, whereby a team disinfects cholera patients' households, and household disinfection kits (HDKs), whereby cleaning materials are provided to cholera patients' family members. Currently, both interventions lack evidence, and international agencies recommend HDK distribution; however, household spraying remains widely implemented. To understand this disconnect, we conducted 14 key informant interviews with international and national responders and a study in Haiti assessing HDK efficacy using two training modules including 20 household surveys and 327 surfaces samples before and after cleaning. During interviews, 80% of the international-level informants discussed evidence gaps for both interventions, and 60% preferred HDKs. Conversely, no national-level informants knew what an HDK was; therefore, they all preferred spraying. Informants discussed behavior changes, bleach perceptions, and implementation as facilitators and/or barriers to implementing both interventions. In households, training with demonstrations regarding the use of HDK led to increased reductions of Escherichia coli (P < 0.001) and Vibrio spp. (P < 0.001) on surfaces after participants cleaned the household compared with a hygiene promotion session only. These results emphasize the gap between the current international-level policy and the realities of cholera response programs, highlight the need for evidence to align household disinfection recommendations, and underscore the importance of the dissemination and training of responders and affected populations regarding methods to prevent intrahousehold cholera transmission.

Transmission dynamics of cholera with hyperinfectious and hypoinfectious vibrios: mathematical modelling and control strategies.

Cholera is a common infectious disease caused by Vibrio cholerae, which has different infectivity. In this paper, we propose a cholera model with hyperinfectious and hypoinfectious vibrios, in which both human-to-human and environment-to-human transmissions are considered. By analyzing the characteristic equations, the local stability of disease-free and endemic equilibria is established. By using Lyapunov functionals and LaSalle's invariance principle, it is verified that the global threshold dynamics of the model can be completely determined by the basic reproduction number. Numerical simulations are carried out to illustrate the corresponding theoretical results and describe the cholera outbreak in Haiti. The study of optimal control helps us seek cost-effective solutions of time-dependent control strategies against cholera outbreaks, which shows that control strategies, such as vaccination and sanitation, should be taken at the very beginning of the outbreak and become less necessary after a certain period.

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.

Modelling cholera transmission dynamics in the presence of limited resources.

OBJECTIVES: We study the transmission dynamics of cholera in the presence of limited resources, a common feature of the developing world. The model is used to gain insight into the impact of available resources of the health care system on the spread and control of the disease. A deterministic model that includes a nonlinear recovery rate is formulated and rigorously analyzed. Limited treatment is described by inclusion of a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings. RESULTS: The model analysis shows that the disease free steady state is locally stable when the threshold [Formula: see text]. It is also shown that the model has multiple equilibria and the model exhibits the phenomenon of backward bifurcation whose implications to cholera infection are discussed. The results are useful for the public health planning in resource allocation for the control of cholera transmission.

Mathematical modelling and numerical simulations of the influence of hygiene and seasons on the spread of cholera.

Cholera is a bacterial disease, its spread is strongly influenced by environmental factors and some socio-economic factors such as hygiene standards and nutrition of the population. This paper is devoted to the modelling of the impact of climatic factors and human behaviour on the spread of cholera. The mathematical modelling incorporates the direct transmission and the indirect transmission due to environmental knowledge. Taking into account the effect of the intra-annual variation of climatic factors on the transmission of cholera, a non-autonomous ordinary differential equations is proposed to describe the dynamics of the transmission of cholera. When the intra-annual variation of climate is not incorporated into the model, the latter becomes autonomous. The basic reproductive number is calculated and the stabilities of equilibria are investigated. In the non-autonomous case, the disease extinction and uniform persistence of disease are investigated. The results suggest that the transmission and spread of cholera can be affected by climatic factors, the proportion of the undernourished individuals and the proportion of people who respect the hygiene standards. Finally, some numerical simulations are proposed using the parameters values of climatic factors and socio-economic factors of some localities situated in Lake Chad border between Chad, Cameroon and Nigeria.

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

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

Disease and disaster: Optimal deployment of epidemic control facilities in a spatially heterogeneous population with changing behaviour.

Epidemics of water-borne infections often follow natural disasters and extreme weather events that disrupt water management processes. The impact of such epidemics may be reduced by deployment of transmission control facilities such as clinics or decontamination plants. Here we use a relatively simple mathematical model to examine how demographic and environmental heterogeneities, population behaviour, and behavioural change in response to the provision of facilities, combine to determine the optimal configurations of limited numbers of facilities to reduce epidemic size, and endemic prevalence. We show that, if the presence of control facilities does not affect behaviour, a good general rule for responsive deployment to minimise epidemic size is to place them in exactly the locations where they will directly benefit the most people. However, if infected people change their behaviour to seek out treatment then the deployment of facilities offering treatment can lead to complex effects that are difficult to foresee. So careful mathematical analysis is the only way to get a handle on the optimal deployment. Behavioural changes in response to control facilities can also lead to critical facility numbers at which there is a radical change in the optimal configuration. So sequential improvement of a control strategy by adding facilities to an existing optimal configuration does not always produce another optimal configuration. We also show that the pre-emptive deployment of control facilities has conflicting effects. The configurations that minimise endemic prevalence are very different to those that minimise epidemic size. So cost-benefit analysis of strategies to manage endemic prevalence must factor in the frequency of extreme weather events and natural disasters.

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

BACKGROUND: Impact evaluation of vaccination programs is necessary for making decisions to introduce oral cholera vaccines (OCVs) in cholera-endemic countries. METHODS: We 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. RESULTS: Data 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. CONCLUSIONS: Periodic 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.

Modelling Optimal Control of Cholera in Communities Linked by Migration.

A mathematical model for the dynamics of cholera transmission with permissible controls between two connected communities is developed and analysed. The dynamics of the disease in the adjacent communities are assumed to be similar, with the main differences only reflected in the transmission and disease related parameters. This assumption is based on the fact that adjacent communities often have different living conditions and movement is inclined toward the community with better living conditions. Community specific reproduction numbers are given assuming movement of those susceptible, infected, and recovered, between communities. We carry out sensitivity analysis of the model parameters using the Latin Hypercube Sampling scheme to ascertain the degree of effect the parameters and controls have on progression of the infection. Using principles from optimal control theory, a temporal relationship between the distribution of controls and severity of the infection is ascertained. Our results indicate that implementation of controls such as proper hygiene, sanitation, and vaccination across both affected communities is likely to annihilate the infection within half the time it would take through self-limitation. In addition, although an infection may still break out in the presence of controls, it may be up to 8 times less devastating when compared with the case when no controls are in place.

Minimizing the Risk of Disease Transmission in Emergency Settings: Novel In Situ Physico-Chemical Disinfection of Pathogen-Laden Hospital Wastewaters.

The operation of a health care facility, such as a cholera or Ebola treatment center in an emergency setting, results in the production of pathogen-laden wastewaters that may potentially lead to onward transmission of the disease. The research presented here evaluated the design and operation of a novel treatment system, successfully used by Médecins Sans Frontières in Haiti to disinfect CTC wastewaters in situ, eliminating the need for road haulage and disposal of the waste to a poorly-managed hazardous waste facility, thereby providing an effective barrier to disease transmission through a novel but simple sanitary intervention. The physico-chemical protocols eventually successfully treated over 600 m3 of wastewater, achieving coagulation/flocculation and disinfection by exposure to high pH (Protocol A) and low pH (Protocol B) environments, using thermotolerant coliforms as a disinfection efficacy index. In Protocol A, the addition of hydrated lime resulted in wastewater disinfection and coagulation/flocculation of suspended solids. In Protocol B, disinfection was achieved by the addition of hydrochloric acid, followed by pH neutralization and coagulation/flocculation of suspended solids using aluminum sulfate. Removal rates achieved were: COD >99%; suspended solids >90%; turbidity >90% and thermotolerant coliforms >99.9%. The proposed approach is the first known successful attempt to disinfect wastewater in a disease outbreak setting without resorting to the alternative, untested, approach of 'super chlorination' which, it has been suggested, may not consistently achieve adequate disinfection. A basic analysis of costs demonstrated a significant saving in reagent costs compared with the less reliable approach of super-chlorination. The proposed approach to in situ sanitation in cholera treatment centers and other disease outbreak settings represents a timely response to a UN call for onsite disinfection of wastewaters generated in such emergencies, and the 'Coalition for Cholera Prevention and Control' recently highlighted the research as meriting serious consideration and further study. Further applications of the method to other emergency settings are being actively explored by the authors through discussion with the World Health Organization with regards to the ongoing Ebola outbreak in West Africa, and with the UK-based NGO Oxfam with regards to excreta-borne disease management in the Philippines and Myanmar, as a component of post-disaster incremental improvements to local sanitation chains.

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

BACKGROUND: Killed, 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 & FINDINGS: We 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. CONCLUSIONS: We 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.

Emerging, evolving, and established infectious diseases and interventions.

Planning, implementing, and evaluating interventions against infectious diseases depend on the nature of the infectious disease; the availability of intervention measures; and logistical, economic, and political constraints. Infectious diseases and vaccine- or drug-based interventions can be loosely categorized by the degree to which the infectious disease and the intervention are well established. Pertussis, polio, and measles are three examples of long-known infectious diseases for which global vaccination has dramatically reduced the public health burden. Pertussis vaccination was introduced in the 1940s, polio vaccination in the 1950s, and measles vaccination in the 1960s, nearly eliminating these diseases in many places.

Assessment of the relationship between bacteriological quality of dug-wells, hygiene behaviour and well characteristics in two cholera endemic localities in Douala, Cameroon.

BACKGROUND: Access to potable water is grossly inadequate in Douala-Cameroon. The situation is worse in slum areas, compelling inhabitants to obtain water from sources of doubtful quality. This has contributed to frequent outbreaks of water-borne diseases particularly cholera, which results in severe morbidity and mortality. Shallow wells are a major source of water in these areas. We analyzed the influence of some factors on the bacteriological quality of well water in Bepanda and New Bell, cholera endemic localities in Douala to generate data that would serve as basis for strengthening of water and health policies. METHODS: Questionnaires were administered to inhabitants of study sites to appraise their hygiene and sanitation practices, and level of awareness of waterborne diseases. The bacteriological quality of water was determined by investigating bacterial indicators of water quality. Relationship between well characteristics and bacteriological quality of water was determined using χ² test. The Kendall tau_b nonparametric correlation was used to measure the strength of association between well characteristics and bacteriological parameters. Statistics were discussed at 95% confidence level. Antibiotic susceptibility of isolates was investigated by the Kirby-Bauer and broth dilution techniques. Multidrug resistant species were tested for extended ß-lactamase production potential. RESULTS: Inhabitants demonstrated adequate knowledge of waterborne diseases but employed inappropriate method (table salt) for well disinfection. Well construction and location violated guidelines. Indicator bacterial counts greatly exceeded the WHO guidelines. Variation in bacteriologic parameters between sites was not significant (P > 0.05) since well characteristics and hygiene and sanitary practices were similar. Differences in bacteriologic quality with respect to state of well, and presence of molded casing and lid, and height of casing were not significant (P > 0.05). Well distance from sanitary structure negatively correlated with bacteriological characteristics indicating it could be a major contributory factor to poor water quality. Bacteria isolated were predominantly enteric organisms. Ciprofloxacin was the most active agent. Extended ß-lactamase producers were detected among Salmonella species, Citrobacter fruendii and E. coli. CONCLUSION: Poor well location, construction, and hygiene and sanitary practices were among the factors affecting water quality. There is an urgent need for education of inhabitants on effective water disinfection strategies and for regular monitoring of wells.

Analysis of occupational infections among health care workers in Limpopo province of South Africa.

OBJECTIVE: Occupational infections particularly hospital-acquired infections (HAIs) are a serious problem in the healthcare industry worldwide. This study purported to investigate their prevalence and risk factors among healthcare workers from Limpopo province of South Africa. METHODS: Cases about occupational infectious diseases of healthcare workers from Limpopo province that were submitted to the Compensation Commissioner from January 2006 to December 2009 were reviewed. RESULTS: The total number of cases of infectious diseases reported during the study period was 56; of these, 83.9% (47) of cases were for tuberculosis, 10.7% (6) for cholera, and 5.4% (3) for chickenpox. Nurses were the most affected. Risk factors associated with the acquisition of infection diseases were as follows. The majority of those infected were female (67.9%), aged over 40 years (57.1%), and who had worked for over 10 years (59.2%). With regard to length of time it took for one to be infected, overall it took 13.6±9.7 years from the year of employment to being infected. This duration was just 5.7±4.2 years in HCWs younger than 40 years versus 18.4±9.0 years in those 40 years and over (p=0.001); and 11.4±10.3 years in nurses versus 17.1±7.8 years in non-professional staff members (p=0.046). Mopani district, situated in a rural setting was the most affected as 24 of the 47 cases of tuberculosis occurred there. CONCLUSION: In conclusion, the most common occupational infection or hospital acquired infection among healthcare workers in Limpopo province of South Africa was tuberculosis. It infected mainly nurses from the rural health district of Mopani. Younger age and being a nurse were significant risk factors associated with being infected early.

A cholera outbreak associated with drinking contaminated well water.

BACKGROUND: Cholera has been a significant public health challenge in many communities. An outbreak of acute diarrheal illness occurred among participants in a wedding ceremony in a village in Qazvin, Iran, in 2008. We conducted an epidemiological, environmental and microbiological investigation to determine the causative agent, source and extent of this outbreak. METHODS: Clinical and environmental samples were collected and analyzed for the presence of diarrhea-causing bacterial organisms, which included Vibrio cholera. The relationship between the strains was determined using enterobacterial repetitive intergenic consensus polymerase chain reaction (ERIC-PCR). RESULTS: The attack rate was 21.8%. Clinical and environmental samples were positive for V. cholerae serotype Inaba. All tested isolates had a similar ERIC-PCR pattern, which indicated that a single clone of V. cholerae was responsible for this outbreak. CONCLUSION: Our findings demonstrated that well water was the source of this outbreak.

Transmission dynamics and control of cholera in Haiti: an epidemic model.

BACKGROUND: Official projections of the cholera epidemic in Haiti have not incorporated existing disease trends or patterns of transmission, and proposed interventions have been debated without comparative estimates of their effect. We used a mathematical model of the epidemic to provide projections of future morbidity and mortality, and to produce comparative estimates of the effects of proposed interventions. METHODS: We designed mathematical models of cholera transmission based on existing models and fitted them to incidence data reported in Haiti for each province from Oct 31, 2010, to Jan 24, 2011. We then simulated future epidemic trajectories from March 1 to Nov 30, 2011, to estimate the effect of clean water, vaccination, and enhanced antibiotic distribution programmes. FINDINGS: We project 779,000 cases of cholera in Haiti (95% CI 599,000-914,000) and 11,100 deaths (7300-17,400) between March 1 and Nov 30, 2011. We expect that a 1% per week reduction in consumption of contaminated water would avert 105,000 cases (88,000-116,000) and 1500 deaths (1100-2300). We predict that the vaccination of 10% of the population, from March 1, will avert 63,000 cases (48,000-78,000) and 900 deaths (600-1500). The proposed extension of the use of antibiotics to all patients with severe dehydration and half of patients with moderate dehydration is expected to avert 9000 cases (8000-10,000) and 1300 deaths (900-2000). INTERPRETATION: A decline in cholera prevalence in early 2011 is part of the natural course of the epidemic, and should not be interpreted as indicative of successful intervention. Substantially more cases of cholera are expected than official estimates used for resource allocation. Combined, clean water provision, vaccination, and expanded access to antibiotics might avert thousands of deaths. FUNDING: National Institutes of Health.