Figure 1.
The Location and Timing of Animal Rabies Cases in Serengeti and Ngorongoro Districts, Northwest Tanzania
(A) Rabies cases in Serengeti (blue) and Ngorongoro (red) districts from January 2002 until December 2006. LGCA = Loliondo Game Controlled Area, NCA = Ngorongoro Conservation Area. Dark gray lines show village boundaries. Populations of humans and domestic dogs are denser in Serengeti district than Ngorongoro (Table 3).
(B) Biweekly time series of rabies cases in each district.
Table 1.
Epidemiological Parameter Estimates
Figure 2.
Observed Frequency Distributions of Important Epidemiological Parameters
(A) The incubation period, (B) the infectious period, and (C) the spatial infection kernel. The best fitting gamma distributions to the data are shown by black lines (see Materials and Methods).
Figure 3.
(A) The distribution of dogs bitten per rabid dog (fitted by a negative binomial distribution with mean = 2.15 [95% CI: 1.95–2.37]; variance = 5.61 [95% CI: 4.63–6.92]; shape parameter k = 1.33 [95% CI: 1.23–1.42]; R0 ∼ 1.1). To calculate R0, we excluded dogs that were killed, tied, or those that disappeared before biting any other dogs. Variability in biting behaviour means that a small number of individuals disproportionately affect transmission and can potentially spark an epidemic, but since most individuals cause few, if any, infections, R0 is low and most introductions quickly die out (Figure 4C).
(B) Exponential epidemic growth in Serengeti (blue, R0 ∼ 1.2) and Ngorongoro (red, R0 ∼ 1.1) districts. The R0 estimates from the epidemic trajectories were relatively insensitive to the period used for fitting the exponential curve. The inset shows the distribution of R0 estimates based on fitting to different regions of the time series.
(C) The effective reproductive number, R, (averaged over three-month intervals) for Serengeti (blue) and Ngorongoro (red) districts measured from reconstructed epidemic trees that incorporate prior knowledge on who infected whom. Dots indicate the number of secondary cases resulting from each primary case (inferred from the composite tree of most likely links, with random jitter to avoid superposition on the y-axis). R0 estimated from these reconstructions (during the period of exponential epidemic growth) was ∼1.1 and ∼1.3 for Serengeti and Ngorongoro, respectively.
Table 2.
Estimates of R0 for Outbreaks of Rabies in Domestic Dog Populations around the World
Table 3.
Demographic Parameters and Population Attributes Estimated from Domestic Dog Populations in Northwest Tanzania
Figure 4.
The Impact of Vaccination on Transmission
(A) The size of village-level outbreaks (defined as at least two cases not separated by more than one month, isolated cases are assumed to be non-persistent introductions) in Serengeti (blue, n = 138) and Ngorongoro (red, n = 20) districts plotted against village-specific vaccination coverage at the outbreak onset. Coverage was extrapolated from a demographic model initialized with village-specific dog population estimates and incorporating village-specific vaccination data. Gray shading and contours correspond to the probability of observing an outbreak of a particular size or less, generated from 10,000 stochastic simulations of rabies transmission for every initial vaccination coverage (contours were calculated conditional upon >1 secondary case occurring). The inset illustrates a village-level example of the susceptible reconstruction used to calculate instantaneous vaccination coverage plotted beside rabies cases in that village.
(B) The distribution of secondary cases per infectious dog as inferred from reconstructed epidemic trees in Serengeti (blue) and Ngorongoro (red) districts, plotted against vaccination coverage in the village where the primary case occurred. Random jitter was added to prevent superposition on the y-axis.
(C) Probability of an outbreak being seeded by an introduced case under different levels of vaccination coverage. Due to heterogeneity in the transmission process outbreaks rarely occur when coverage is maintained above Pcrit. However if infections are frequently imported from outside the vaccinated region, at least 40% coverage would need to be maintained to reduce the probability of subsequent outbreaks (of at least ten cases) to <0.05.