Ashleigh R. Tuite, MSc, MPH; Joseph Tien, PhD; Marisa Eisenberg, PhD; David J.D. Earn, PhD; Junling Ma, PhD; David N. Fisman, MD, MPH
Haiti is in the midst of a cholera epidemic. Surveillance data for formulating models of the epidemic are limited, but such models can aid understanding of epidemic processes and help define control strategies.
To predict, by using a mathematical model, the sequence and timing of regional cholera epidemics in Haiti and explore the potential effects of disease-control strategies.
Compartmental mathematical model allowing person-to-person and waterborne transmission of cholera. Within- and between-region epidemic spread was modeled, with the latter dependent on population sizes and distance between regional centroids (a “gravity” model).
Haiti, 2010 to 2011.
Haitian hospitalization data, 2009 census data, literature-derived parameter values, and model calibration.
Dates of epidemic onset and hospitalizations.
The plausible range for cholera's basic reproductive number (R0, defined as the number of secondary cases per primary case in a susceptible population without intervention) was 2.06 to 2.78. The order and timing of regional cholera outbreaks predicted by the gravity model were closely correlated with empirical observations. Analysis of changes in disease dynamics over time suggests that public health interventions have substantially affected this epidemic. A limited vaccine supply provided late in the epidemic was projected to have a modest effect.
Assumptions were simplified, which was necessary for modeling. Projections are based on the initial dynamics of the epidemic, which may change.
Despite limited surveillance data from the cholera epidemic in Haiti, a model simulating between-region disease transmission according to population and distance closely reproduces reported disease patterns. This model is a tool that planners, policymakers, and medical personnel seeking to manage the epidemic could use immediately.
Haiti is in the midst of a cholera epidemic. Surveillance data to inform public health decision making are limited.
The authors constructed a mathematical model of epidemic dynamics that is based on both population and distance. The model's results closely match the contour of the epidemic to date. The model was used to project the probable effect of different approaches to allocation of vaccines and clean water on the course of the epidemic.
The model does not include the effect of antibiotic treatment on transmission of cholera.
A publicly available tool to assist in managing the cholera epidemic in Haiti has been developed and can be further modified and refined.
For each of the 10 departments in Haiti, the population is divided into “susceptible,” “infectious,” and “recovered.” Infection spreads through contact of susceptible with infectious persons both within a given department and in other departments, as well as through contamination of water sources. Additional model details are provided in the Appendix.
Appendix Table 1.
Appendix Table 2.
Close correlation is observed between model projections and reported dates of epidemic onset by region. MSPP = Ministère de la Santé Publique et de la Population.
The model was well-calibrated to reported cumulative hospitalizations. MSPP = Ministère de la Santé Publique et de la Population.
Timing is based on 1000 stochastic simulations, as described in the text. An increasing intensity of color denotes more simulations projecting that region's epidemic to peak at a given time. The epidemic in Artibonite, home of the initial outbreak, is projected to peak first; epidemics in Grand'Anse, Nippes, and Sud are projected to peak last.
Top. Optimized allocation was always more effective than either equal or proportional allocation of vaccine, although the difference between strategies increased with delay in vaccination. Bottom. Compared with allocation of clean water, vaccination was projected to reduce far more cases of cholera.
Appendix Table 3.
The combination strategy demonstrates a superadditive effect.
Optimized allocation of vaccine focuses largely on Ouest department, because of its large population, and Centre department, which serves as a “crossroads” for cholera spread. As vaccination is increasingly delayed, larger shares are allocated to peripheral regions where epidemics occurred later. Numbers in parentheses represent the ordering of outbreaks.
A best-fit model (dotted line) incorporating an R0 of 2.90 and discounted at a rate of 1.8% per day reproduces reported cumulative hospitalizations well. Estimated values for the reproductive number by time are plotted. The reproductive number may have fallen below 1.0 in mid-December; <1.0 is no longer associated with exponential growth (11). The gap between case counts with the discounted model, and models in which the reproductive number (2.78 [base case] and 2.90) is reduced only through depletion of susceptible persons through infection provides an index of the effect of disease-control interventions in Haiti to date. MSPP = Ministère de la Santé Publique et de la Population; R0 = basic reproductive number.
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Tuite AR, Tien J, Eisenberg M, Earn DJ, Ma J, Fisman DN. Cholera Epidemic in Haiti, 2010: Using a Transmission Model to Explain Spatial Spread of Disease and Identify Optimal Control Interventions. Ann Intern Med. 2011;154:593-601. doi: 10.7326/0003-4819-154-9-201105030-00334
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Published: Ann Intern Med. 2011;154(9):593-601.
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