provides estimates of the basic reproductive number (
), and partial reproductive numbers due to “fast” human-to-human transmission (
) and “slow” transmission through the environment (
); it also provides data on the corresponding minimum vaccination coverage needed for a cholera vaccine with an estimated 78% efficacy7
for the 10 departments and the country as a whole. The cumulative cholera cases were fit with mathematical models for each department and for the whole country (). The results in show that Artibonite department had the highest
(2.63) and environmental transmission accounted for most of the transmission (≈ 97%) compared to lower values (≈ 9–55%) in other departments. Artibonite department was the first to report cholera cases1
and epidemiological studies have revealed that, the contamination of the Artibonite River and its tributaries (i.e.
sources of drinking and cooking water for villagers) triggered the epidemic8
. Thus our estimates support the notation that contamination of drinking water sources sparked the outbreak in Artibonite. These results also show that departments neighboring Artibonite had slightly higher
values (1.37–1.73) compared to other departments (1.06–1.44), suggesting that it was the epidemic focal point. Our analysis showed that
estimates are determined by the time scales of the unfolding epidemic i.e.
with fast growing epidemic curves giving a higher percentage of
and vice-versa. However the inference about the estimates of
is likely more robust than the estimates of the individual transmission components (i.e.
). Aggregated cholera data for Haiti compared with the department estimates will, on average, overestimate the required country-wide vaccination coverage by about 20% (). Thus for effective disease control, surveillance and resource allocation there is a need to quantify the magnitude of cholera outbreaks using data on a finer resolution. Analysis of data on a finer grain would likely reveal additional heterogeneities in transmission, but the spatial scales at which it is appropriate to aggregate data for the purposes of planning control interventions remain poorly understood. Since cholera vaccines have different efficacies9,10,11,12
, we also carried out sensitivity analysis to show possible scenarios that may arise from using different types of vaccines by considering an efficacy range of 50–100%.
Cholera model fitting for the cumulative cholera cases where the bold green lines represent the model fit and the blue circles mark the reported data for the cumulative number of cholera cases in the departments for 1000 runs.
The results suggest that a vaccine with 50% efficacy may result in cholera control in most of the departments except for Artibonite, which would require a vaccine with at least 65% efficacy (). However most of the new-generation cholera vaccines have shown an efficacy more than 65%7,9,10,11,12
for periods sufficient to contain epidemic cholera (i.e.
depending on vaccination coverage). But, there are still concerns that most of the studies on vaccine effectiveness were conducted in cholera endemic areas with some degree of immunity within the population, thus these study results may not hold for Haiti where the population was initially immunologically naïve to the disease13,14
Sensitivity analysis of vaccination efficacies from 50%–100% and the corresponding percentage coverage's in the departments and the whole country. Ouest department includes Port-au-Prince and Ouest** hospitalized cases
values illustrate the differences in transmission across Haiti (). Reproductive numbers were estimated separately for Port-au-Prince (), and the part of Ouest that does not include Port-au-Prince, as in the data sets on the MSPP website15
. We also estimated the reproductive number for the whole Ouest department, combining hospitalized cases from both Port-au-Prince and Ouest**, which was used for mapping ().
Figure 2 Map of Haiti showing corresponding values in the departments.
We performed sensitivity analysis using a deterministic version of our model to ascertain the robustness of our
estimates. We carried out sensitivity analysis of κ
(the 50% infectious dose for environmental exposure) and χ (the rate of environmental contamination by cholera infected individuals). On the basis of studies conducted by our group in Lima and Bangladesh, peak environmental counts of ctx-positive V. cholerae
from pristine areas have been found to range from 101
; even in areas with heavy sewage contamination, peak environmental counts of ctx
-positive V. cholerae
were not observed to exceed 106
. The infectious dose for media-grown V. cholerae
ingested by healthy North American volunteers ranges from 108
cfu/mL; this drops to 104
when the inoculum is given with bicarbonate or food18,19,20
. In a series of studies conducted at the Center for Vaccine Development, University of Maryland, the “standard” V. cholerae
inoculum in challenges employing health North American volunteers was 106
, administered with bicarbonate20
In the context of these data, we carried out sensitivity analysis to explore the effects of κ
estimates. Results using aggregated data for Haiti are shown in , which is a plot of estimated
and corresponding values of κ. Varying κ in a plausible range of 105
to 1.5 × 109
cells/ml, which covers the concentration range of vibrios in sewage-contaminated water and also falls within the range of the infectious dose (with bicarbonate, or food) demonstrated among North American volunteers19,20
, we note that
estimates will change by less than 1%. However, these estimates will change by about 13% in vibrio concentration ranging from 1.5 × 109
cells/ml. In we present sensitivity analysis results on the effects of χ
estimates by plotting estimated
and corresponding values of χ
. This parameter may be influenced by a number of socio-economic factors, including adequacy of sewage disposal, and consequently may vary within communities. The distribution of exposure doses would be, in all likelihood, highly skewed. In , we note that a change in χ
from 1 to 100 only affects our estimates by approximately 3%. Thus, while there may be uncertainty around estimates for κ
, changes in these parameters do not substantially affect our results. The discontinuities in and explain points where the curves stops being sensitive to changes in the parameters and the fitting procedure abruptly switches to favor the
Figure 3 The relationship between the basic reproductive number estimate () and κ using aggregated data for Haiti using population sizes in and parameter values in .
Figure 4 The relationship between the basic reproductive number estimate () and χ using aggregated data for Haiti using population sizes in and parameter values in and varying χ from 1 to 100.
In addition, we also explored the effects of other forms of unreported cholera infection such as asymptomatic colonization on
by assuming that the current data represent a certain percentage of reported cases in the clinical spectrum of cholera infection, and then fitting the model to Haitian data. Here, we extend our basic cholera model to incorporate a class of cholera asymptomatic cases as a proportion of total infections. We fit cholera reported data to the class of symptomatic cases in the model based on the assumption that the available reported data only represent a percentage of the total cholera cases. This model also assumes that asymptomatic patients, who shed approximately 103
vibrios per gram of stool for only one day, do not significantly contribute to cholera infection21
. Studies in the early 1970s suggested infection with cholera strains of classical biotype (responsible for the sixth cholera pandemic) resulted in severe cholera cases in only 11% of total infections; 59% of infections were asymptomatic and the remainder represented illness of mild to moderate severity. Other studies during the same period showed that only 2% infected with seventh pandemic biotype El Tor strains had severe disease, and 75% of infected persons were asymptomatic22,23
. However; recent studies have noted substantial increases in the percentage of patients with severe dehydration24
, and the percentage of asymptomatic infected patients appears to be much smaller (<50%, in a recent study by Harris et al.
), attributed to genetic changes in the organism26,27
. Based on these studies we carried out sensitivity analysis to assess the effects of varying the percentage composition of reported symptomatic cases in the range 15–100% on the basic reproductive number. The range of the percentage composition of reported symptomatic cases (15–100%) considered here is consistent with recent findings which suggest an increase in the percentage of severe cases24
and a smaller percentage of asymptomatic carriage (<50%)25
. The results in show that incorporating other forms of unreported cholera infection into the model changed
estimate by less than 5%.
Figure 5 The relationship between and the percentage composition of reported symptomatic cholera cases reported using aggregated data for Haiti, parameter values from , and population size from .