We calibrated the simulation model using cholera incidence data observed in the first year of the vaccine trial () over a 180 d period in order to capture all the cholera transmission during the large annual cholera outbreak. This was done by varying the transmission probability, π (see Figure S6
and Text S2
), such that the differences between the observed incidence rates and the simulated incidence rates in were minimized. The estimated reproductive number was 5.0 with a standard deviation of 3.3 (see Text S2
). A summary of the parameters and their baseline values are shown in Table S1
. The vaccine coverage levels in the target population and the effective coverage in the entire population from the trial are summarized in . We assume that vaccinated people receive an effective regimen of two doses. The observed cholera incidence rates among the unvaccinated ranged from a high of 7.0 cases/1,000 over 180 d for the subregions with the lowest coverage in the target population, centered at 14%, to 1.5 cases/1,000 for the highest coverage, centered at 58%. The observed cholera incidence rates among the vaccinated ranged from a high of 2.7 cases/1,000 for the subregions with the lowest coverage to 1.3 cases/1,000 for the highest coverage. We set the vaccine efficacy (VE) for susceptibility to VES
= 0.7 [2
] and for infectiousness to VEI
= 0.5. The simulated incidence rates provided a good fit to the data based on a χ2
goodness-of-fit test for frequency data (p
= 0.84, 9 degrees of freedom). A–D show the number of cases over time comparing the unvaccinated to the vaccinated populations. Videos S1
show the spatial–temporal epidemics at different coverage levels. For effectiveness measures, we compare the intervention subregions to hypothetical subregions that receive no vaccine, i.e., f
= 0. shows the indirect, total, and overall effectiveness estimated by the model for possible coverage levels when comparing coverages in the entire population, 2 y of age and older, ranging from 10% to 90% compared to no vaccination. For example, the average indirect effectiveness, comparing a population with a coverage of 30% to one with no vaccination, is 70% (also see Figure S7
). This indicates that on average, the cholera incidence among unvaccinated people in a population with 30% coverage would be reduced by 70% compared with a completely unvaccinated population. At this level of coverage, the total effectiveness of 90% indicates high protection for a vaccinated person in a population with 30% vaccination coverage, while the overall effectiveness of 76% indicates a good overall reduction in risk to the overall population. According to the model, around 40 cases of cholera are prevented per 1,000-dose regimens of vaccine at low coverage and 13 cases at high coverage. At coverage levels of 50% and higher, all levels of effectiveness exceed 85%, resulting in the nearly total control, i.e., an overall annual cholera incidence of about 1 case per 1,000 people, of cholera transmission.
Vaccination Coverage, Average Incidence Rates, and Direct Effectiveness (Calibration Runs)
Simulated Number of Cholera Cases per 1,000 over a 180-Day Period in the Matlab Study Population for a Single Stochastic Realization
Average Indirect, Total, and Overall Effectiveness of Vaccination, and Cases Prevented Per 1,000-Dose Regimens
From , we see that the simulated direct effectiveness at all coverage levels is estimated from the simulations to be about 66%, while the vaccine efficacy for susceptibility, VES
is pre-set at 70%. This small underestimation is due to the fact that we model the vaccine effect to be a 70% reduction in the risk of infection per contact with an infective source, i.e., a leaky effect, but we use the risk ratio estimator of vaccine effectiveness over the entire cholera epidemic. We do this for the purpose of comparison, as this was the primary estimator used in the cholera vaccine trial in Matlab [2
]. We have shown that an estimator based on the monthly hazard ratio gives a similar, but more accurate estimate of actual vaccine efficacy [3
]. Also note from that the observed estimate of the direct effectiveness is only 14% in the highest vaccination coverage category when it should be around 66%. This discrepancy probably reflects small sample bias due to the low cholera incidence in the highest vaccine coverage category.
shows the overall effectiveness estimated by the model for possible coverage levels in populations at different levels of relative susceptibility compared to Matlab. For populations that are 1.5 times as susceptible as those in Matlab, 50% coverage would still be sufficient to achieve an overall effectiveness of 80%. However, for populations that are 2–2.5 times as susceptible, 70% vaccine coverage would be necessary to achieve control.
Average Overall Vaccine Effectiveness When Varying Relative Susceptibility
Since vaccine efficacy can vary for different field settings and vaccines, a sensitivity analysis was carried out on the VES
and the VEI
to determine the minimum efficacy needed to maintain control at the vaccine coverages explored above. The VES
were varied from 0.3 to 0.8 (Figures S8
). These analyses reveal that theVES
could be as low as 0.5 and the VEI
as low as 0.3 to still maintain control of cholera, as long as the vaccine coverage were 50% or higher. Further sensitivity analysis on the vaccine coverage (Figures S13
) reveals that vaccine coverage should be at least 50% to maintain control.
Sensitivity analyses also were performed for values of the seasonal boost factor, the relative infectiousness of symptomatic infectives, and varied subregion sizes. The baseline epidemic with no vaccination was calibrated to the simulated cholera incidence data for Matlab with no vaccination. Our result that in populations like Matlab 50% vaccine coverage should be sufficient to control cholera remains valid for variation in the season boost factor (Figure S16
) and relative infectiousness (Figure S17
). However, we did see variation with respect to subregion size. For larger subregions (>6 km2
each), 50% vaccine coverage was sufficient for control. But for very small subregions (0.04 km2
each), the average overall vaccine effectiveness approaches 75% with a vaccination coverage of 70% (Figure S18
). This lower effectiveness implies that random mass vaccination may not be effective in small subregions, and vaccination would have to concentrate on the small subregions where transmission is occurring. This result could be applicable to epidemic cholera in small, dense settings such as refugee camps where coverage would have to be high to control transmission.