Rabies shows how scale of transmission can enable acute infections to persist at low prevalence

Abstract

How acute pathogens persist and what curtails their epidemic growth in the absence of acquired immunity remains unknown. Canine rabies is a fatal zoonosis that circulates endemically at low prevalence among domestic dogs in low- and middle-income countries. We traced rabies transmission in a population of 50,000 dogs in Tanzania from 2002 to 2016 and applied individual-based models to these spatially resolved data to investigate the mechanisms modulating transmission and the scale over which they operate. Although rabies prevalence never exceeded 0.15%, the best-fitting models demonstrated appreciable depletion of susceptible animals that occurred at local scales because of clusters of deaths and dogs already incubating infection. Individual variation in rabid dog behavior facilitated virus dispersal and cocirculation of virus lineages, enabling metapopulation persistence. These mechanisms have important implications for prediction and control of pathogens that circulate in spatially structured populations.

Understanding the processes that regulate endemic disease dynamics remains a long-standing challenge in epidemiology (1, 2), and the mechanisms that enable long-term persistence at low prevalence remain largely unexplored (3). This is particularly true for canine rabies, a fatal zoonotic virus for which naturally acquired immunity has not been demonstrated. The basic reproductive number R₀ of rabies, which is defined as the expected number of secondary cases produced by a typical infectious individual in a fully susceptible population (4), is low (between 1.1 and 2) and is relatively insensitive to dog density (5), making the disease amenable to elimination through dog vaccination (6). Yet dog-mediated rabies remains endemic across Africa and Asia, where it kills tens of thousands of people every year (7), and its persistent circulation at such low prevalence in largely unvaccinated populations is an enduring enigma.

Rabies is, however, a usually tractable system for understanding how population-level patterns of infection emerge from pathogen transmission at the individual level. Rabies is transmitted through bites, which can often be observed, and the clinical signs are readily identifiable, with infected animals typically dying within 1 week of disease onset (Fig. 1E). Capitalizing on these distinctive characteristics, we conducted exhaustive contact tracing to generate spatially resolved data on rabies infection and transmission in Serengeti district, Northern Tanzania, between January 2002 and December 2015. Serengeti district adjoins other populated districts to the north and west and Serengeti National Park to the southeast (Fig. 1A). We previously showed that domestic dogs maintain rabies in this part of Tanzania, with infrequent spillover to wildlife and spillback to domestic dogs (8). In Serengeti district’s population of around 50,000 dogs (and 250,000 people), we traced 3612 rabies infections (comprising 3081 cases in dogs, 75 in cats, 145 in wildlife, and 311 in livestock) (Fig. 1), along with 6684 potential transmission events to other animals and 1462 people bitten by rabid animals, of whom 44 died from rabies. Most identified cases could be statistically linked to plausible progenitors, indicating that contact tracing detected most cases. Further analysis indicated that 83 to 95% of cases were detected, with missed cases mainly being those generating limited, if any, onward transmission (9). These data show that despite local vaccination effort (coverage varying between 10 and 40%) (fig. S3B), rabies circulated continuously, with a maximum prevalence of just 0.15%.

Fig. 1. Rabies in Serengeti district.

(A) Mapped cases are in red. Shading indicates dog density, and lines indicate village boundaries. (Inset) The district location in Tanzania. (B) Monthly time series of cases in domestic dogs (red; n = 3081) and other carnivores (gray, n = 214). Species are detailed in (9). (C) Dogs bitten per rabid dog versus dog density at each rabid dog’s location (1-km² scale), showing no apparent relationship. The red line indicates the generalized additive model prediction, and gray lines indicate the standard error; P > 0.05. (Inset) The proportional distribution of the dog population and of case locations in relation to dog density on a log scale. Squares indicate mean dog population density (black; 23 dogs/km²) and mean dog density at case locations (red; 41 dogs/km²), indicating higher per capita incidence in higher-density areas (independent samples t test on log-transformed data, T = 22.45, P < 2.2 × 10⁻¹⁶). (D and E) Distributions of (D) rabid dog step-lengths between contacts and (inset) distances to contacts and (E) serial intervals and (inset) infectious periods. The best-fitting distributions are in red (table S1), with step-lengths and distances censored for animals with unknown starting locations (9). (F) Dogs bitten per rabid dog from contact tracing (gray) and simulated from the individual-based model (red; 5th to 95th percentiles). The y axis is square root transformed in (D) and (F) to better illustrate extreme values.

Endemic diseases are thought to be primarily regulated by the depletion of susceptible hosts, typically through disease-induced (or vaccine-acquired) immunity, counterbalanced by births of susceptibles and deaths (4). Yet the very low prevalence and absence of acquired immunity for rabies indicates that large-scale depletion of susceptible hosts is negligible, challenging this explanation as a mechanism for persistence. We estimated dog densities at high spatial resolution through a district-wide census, georeferencing almost 36,000 households and recording the vaccination status of dogs [in this setting, almost all dogs are owned but also free-roaming, and there are no feral dogs (10)]. Although we saw no clear relationship between dog population density and contact rate when examining dogs bitten per rabid dog (Fig. 1C), mapping rabies infections revealed a small yet significantly higher incidence of cases in higher-density areas (Fig. 1C), which suggests density-dependent processes. These observations are difficult to reconcile: How does transmission respond to dog population density, and what processes keep prevalence so low?

We propose that understanding the fine-scale structure of rabies transmission networks is critical to explaining its persistent dynamics and can inform its control and eventual elimination. We used the serial interval distribution—defined as the interval between the onset of infection in primary and secondary cases—and movement of traced rabid dogs to reconstruct transmission trees, comprising putative introductions into the district and descendent chains of transmission. Over the 14 years, we estimated around 238 introductions (8 to 24 per year) that led to onward circulation, most likely spreading from neighboring villages (movie S1). Twenty-two transmission chains, accounting for >70% of cases, circulated for more than 12 months (including two for more than 4 years), illustrating how cocirculation of lineages contributes to persistence within a metapopulation (Fig. 2). We applied an individual-based model, seeded by these introductions, to the spatially resolved case and dog density data to investigate the processes that modulate transmission, the scale over which they operate, and how they facilitate these metapopulation dynamics.

Fig. 2. The spatiotemporal distribution of transmission chains.

(A) Monthly cases, estimated to be between 83 and 95% of all cases in the district. The 11 chains with most cases are highlighted in color, and all smaller chains (<58 cases) are shaded gray. (B) Spatial distribution of monthly cases, from the consensus tree of 1000 bootstrapped reconstructions (9).

We examined the effect of host (dog) density on contact (biting) within our stochastic individual-based model, drawing from predatorprey functional response theory (11), to fit parameters defining the transmission process in relation to host density (12). We fitted the parameters assuming that susceptible and infected dogs were well mixed at different scales, ranging from the whole district to within 0.25-km² grid cells (fig. S2). The best-fitting parameters at each scale differed in their simulation outcomes. Only models at the 1-km² scale reliably reproduced observed dynamics and captured emergent population- and individual-level properties (Figs. 1F and 3A and fig. S10). We conclude that the processes that regulate the size of outbreaks and overall prevalence of rabies operate primarily on scales that are much smaller than those typically modeled for this disease.

Fig. 3. Time series of rabies cases and simulated counterfactual scenarios.

Observed cases (red), with interquartile (dark shading) and 95% (light shading) prediction intervals, both computed pointwise, from simulations at the 1-km² scale, and with three illustrative example runs (dark lines). The simulated scenarios are (A) with vaccination campaigns as implemented, (B) under low vaccination coverage, (C) with vaccination campaigns as implemented but no individual heterogeneity in contact parameters, and (D) without incursions after the first year.

Our modeling shows that epidemic growth is curtailed in two ways: from deaths of rabid dogs reducing contact opportunities and through redundant exposures of dogs already incubating infection. These processes increasingly stem transmission in lower-density areas, where dogs have fewer contact opportunities (Fig. 4). Simulations of index infections to estimate R₀ (in an entirely susceptible population) show that rabid dogs bite, on average, 2.91 dogs, leading to approximately 1.47 secondary cases per index case [95% percentile intervals (PI) 1.39 to 1.56]. This R₀ value is slightly higher than previously estimated (5), in part because of population growth (median dog density increased from 12 to >20 dogs/km² over the 14 years) but varies across the landscape in relation to dog densities (Fig. 4) and according to how it is measured; estimates simulated from dogs sampled from the landscape (by grid cell, rather than in proportion to density) were slightly lower (1.35, 95% PI 1.27 to 1.43), whereas estimates from dogs sampled from the transmission network were slightly higher (1.48, 95% PI 1.38 to 1.58) because more cases occur in higher-density grid cells (Fig. 4) (9).

Fig. 4. Rabies transmission in relation to population density.

(A) Distribution of dog densities in Serengeti district on a log scale. (B) Holling curves computed from the most reliable parameter set at each scale (9), with contact rate rescaled by the median infectious period (2 days) and dog density on a log scale. Gray shading indicates dog densities below the median (16.4 dogs per km²) midway through the period (median density increased from 12 to 22 dogs/km² over the 14 years). (Inset) Replotted on a linear scale. At the optimal spatial scale (red line; 1 km²), contact rates are density dependent at low dog densities and become increasingly densityindependent at higher densities. Parameter sets at other scales failed to reliably generate the observed dynamics. The Holling curve indicates how even removal of a small number of susceptible dogs locally (from rabies deaths or incubating infection) reduces transmission so that R approaches 1, which corresponds to around two contacts per infection (horizontal line), with half developing rabies. (C) Histogram of R₀ estimates from simulating index infections (9), either by location (blue), density (orange), or from the transmission network (red). (D and E) Mapped (D) R₀ estimates and (E) dog density at the midpoint.

Under endemic circulation, the effective reproduction number, R, declines by just over 30% and remains near 1. Around 78% of this reduction is from recent rabies deaths removing potential contacts, and 22% is from reexposures of already incubating dogs. Thus, infected dog movement (fig. S1) determines the scale of mechanisms that regulate endemic dynamics, so that even small outbreaks (approximately five cases per square kilometer) can result in substantive reductions in R, given the heterogeneous distribution of dogs on the landscape (Fig. 4). There remains ambiguity in the mechanisms that underpin density-independent transmission at higher dog densities. Human responses likely play a role (45% of traced rabid dogs were either killed or tied) and are to some extent captured in our model, but these may operate differently during larger outbreaks (beyond those observed) and in more urbanized populations (<2% of dogs in this rural district live at densities >100 dogs/km²). Our data highlight how better understanding of functional responses that describe theoreticalrelationships of transmission with density (10, 11) are needed to predict endemic pathogen dynamics.

Individual variation in disease transmission causes rare but more explosive outbreaks and more frequent extinctions (13). We observed considerable variation in rabid dog behavior (Fig. 1), with a few rabid dogs biting many others (4% of rabid dogs bit >10 other dogs each, and four bit >50 dogs) and running long distances (nine rabid dogs ran >10 km to contact other animals). Overdispersion in the size of transmission chains (fig. S11) reflects this variability in rabid dog behavior and thus makes persistence more remarkable (13). Our modeling captured this individual heterogeneity (Fig. 1F), revealing its relevance for rabies dynamics: In counterfactual simulations without individual heterogeneity, rabies incidence was reduced by around 50% (fig. S7C) and the (relatively) large outbreaks observed in nature and in simulations with heterogeneity did not occur (Fig. 3, C versus A). The biological drivers of this variation result predominantly from individual-level (13) rather than environmental or population-level differences (14, 15),such as host density, but are poorly understood. Behavioral manifestations of infection that depend on sociological and pathological factors, such as exposure dose and sites of viral proliferation (16), might underpin this individual-level variation.

Both the scale of and heterogeneity in contact and movement are crucial to capturing rabies dynamics (Fig. 3). Density-dependent transmission processes, although well described theoretically (2, 17), are extremely challenging to quantify in relation to spatial scale. This may explain why few empirical studies of directly transmitted diseases have found evidence of strong density-dependent transmission (18–20). For rabies, the main susceptible depletion mechanisms—deaths of rabid dogs and reexposures of dogs already incubating infection—only curtail transmission if infection is clustered and explain why nonspatial models of rabies do so poorly at replicating dynamics, because rabies incidence is negligible at the population-level. Clustering has been shown to reduce pathogen transmission through build-up of immune individuals (13), as well as in the context of redundant biting by insect vectors of disease (21); it has also been theorized to reduce transmission in the early stages of epidemics (22). For rabies, the incubation period acts in a way similar to that of immunity, resulting in redundant exposures that limit transmission. Natural immunity is not generally considered relevant in canine rabies or required to explain persistence, but antibodies have been detected in healthy unvaccinated dogs (17). If short-lived immunity does follow aborted infections, as may be the case for vampire bat rabies (18), our expectation is that it would cluster in the same way as incubating infections do, reinforcing local-scale effects. Clustering has been demonstrated to make outbreaks less explosive and to extend persistence (19), yet the potential relevance of such microdepletion mechanisms to many pathogens may be underestimated because their measurement relies on sufficiently resolved datasets. Our conclusion, that the relevant spatial scale at which to consider host density is determined by the scale of movements of infectious hosts, offers a starting point for the appropriate spatial scale at which to model other pathogens for which spatially detailed data are lacking.

Our analyses further illustrate the degree to which introduced cases contribute to rabies persistence. In the absence of introductions and under observed levels of vaccination, we expect infection to circulate in the Serengeti district for up to 7 years, typically dying out within 4 years (Fig. 3D). But, with between 8 to 24 rabid dogs arriving each year from neighboring villages, infection persists even under reasonable vaccination coverage, even though most cause only short-lived chains of transmission (fig. S10). In settings where vaccination coverage is negligible (dog populations across much of Africa and Asia), our simulations indicated a mean duration of outbreaks from single introductions of between 10 and 30 weeks; however, the maximum exceeded 12 years (fig. S10). Locally self-limiting clusters of cases recur on the landscape (movie S1) and, in combination with heterogeneous movement and contact, permit the invasion and cocirculation of multiple lineages (Fig. 2) (20). Recurrent introductions and extinctions have been reported in many endemic settings (21–23), and cross-border introductions have led to rabies emergence in several previously rabies-free areas (24–28). In contrast to diseases such as mosquito-transmitted Dengue (29), chains of infection circulate largely independently, given the low prevalence of cases and very localized susceptible depletion. The concurrent extinction of all lineages therefore becomes less probable as more chains of infection cocirculate.

From a practical perspective, our findings explain why dog culling has typically been so ineffective for controlling rabies; dog populations would need to be reduced below very low densities across all areas where infection is circulating. Culling more than 50% of the 400,000 dogs in Flores, Indonesia, had no apparent impact on rabies circulation (30). Our results reinforce the message that mass dog vaccination remains the most effective and feasible method of controlling rabies and provides insights that should inform elimination strategies. Simulations indicate that although dog vaccinations prevented more than 4000 animal cases, 2000 human rabies exposures, and 50 deaths in the Serengeti district, introductions continually seeded new foci, with scaled-up dog vaccination (beyond the district) required to achieve elimination (Fig. 3). Infrequent longer-distance movements of rabid dogs seed outbreaks in unaffected localities across heterogeneously distributed populations, leading to localized flare-ups where vaccination coverage is not maintained. The resulting low prevalence persistence presents a challenge for elimination, given that surveillance is very weak in most rabies-endemic regions. Yet the concurrent circulation of viral lineages offers an opportunity for using increasingly affordable genomic approaches to assess the performance of both rabies surveillance and control (31). Differentiating undetected circulation from reintroductions will be necessary as control efforts are scaled up toward the 2030 goal of zero human deaths from dog-mediated rabies (32).

Data and materials availability

Code to reproduce the analyses together with deidentified data are available at (33).