Synchrony of sylvatic dengue isolations: a multi-host, multi-vector SIR model of dengue virus transmission in Senegal

Abstract

Isolations of sylvatic dengue-2 virus from mosquitoes, humans and non-human primates in Senegal show synchronized multi-annual dynamics over the past 50 years. Host demography has been shown to directly affect the period between epidemics in other pathogen systems, therefore, one might expect unsynchronized multi-annual cycles occurring in hosts with dramatically different birth rates and life spans. However, in Senegal, we observe a single synchronized eight-year cycle across all vector species, suggesting synchronized dynamics in all vertebrate hosts. In the current study, we aim to explore two specific hypotheses: 1) primates with different demographics will experience outbreaks of dengue at different periodicities when observed as isolated systems, and that coupling of these subsystems through mosquito biting will act to synchronize incidence; and 2) the eight-year periodicity of isolations observed across multiple primate species is the result of long-term cycling in population immunity in the host populations. To test these hypotheses, we develop a multi-host, multi-vector Susceptible, Infected, Removed (SIR) model to explore the effects of coupling multiple host-vector systems of dengue virus transmission through cross-species biting rates. We find that under small amounts of coupling, incidence in the host species synchronize. Long-period multi-annual dynamics are observed only when prevalence in troughs reaches vanishingly small levels (< 10(-10)), suggesting that these dynamics are inconsistent with sustained transmission in this setting, but are consistent with local dengue virus extinctions followed by reintroductions. Inclusion of a constant introduction of infectious individuals into the system causes the multi-annual periods to shrink, while the effects of coupling remain the same. Inclusion of a stochastic rate of introduction allows for multi-annual periods at a cost of reduced synchrony. Thus, we conclude that the eight-year period separating amplifications of dengue may be explained by cycling in immunity with stochastic introductions.

Figure 1. Summary of dengue, yellow fever and chikungunya isolates, 1962–2008.

Panel A shows number of dengue, yellow fever and chikungunya virus isolates over time by species. Scales at right indicate number of isolations. Blue boxes on dengue heatmap indicate sylvatic human isolations reported in Diallo et al. (2003). Dashed black lines separate mosquito isolations from primate isolations. Panels B, C and D show the Fourier power spectrum with Daniell smoothers of (3,3) with 95% bootstrap confidence intervals for the aggregated dengue, yellow fever and chikungunya virus isolates, respectively. A detailed description of surveillance methods has been published previously .

Figure 2. Diagram of SIR model.

The model incorporates two primate species and two mosquito species that are coupled through the blue and red cross-biting rates. Each mosquito species is assumed to have a preferred host; these transmissions are represented in black. Each transmission term incorporates two aspects: one, a biting rate between mosquito and primate which is symmetric (e.g. “mosquito 2 to primate 1”), as well as a seasonally-varying probability of infection term which is asymmetric for primates and mosquitoes. Primates recover at rate “recovery”. Mosquitoes and primates birth and death rates are represented in grey (labeled “birth” and “death”, respectively). See the text for more detail, and the Supporting Information S1 for model equations.

Figure 3. Effect of demographics on model dynamics with and without constant introduction.

This figure displays the effects of changing transmission probabilities (x-axis) and 1/primate birth rates (y-axis). Panels A and B are heatmaps of the period of peak Fourier spectral densities in the 1-host, 1-vector systems, with and without per year rate of infection introduction, respectively. Circles indicate example epidemic time series shown in panels C–H. Contour lines are analytically calculated values of (see Supporting Information S1). Other parameters held fixed: , , , , and .

Figure 4. Prevalence in large and small primates in the coupled and uncoupled systems without constant introduction.

Panels A and B show results for models with coupling, E and F for uncoupled models. Panel A and E characterize the dynamics of dengue in the large primate species, B and F dengue dynamics in the small primate species. Coupled models (A, B, C and D) are coupled at 1/500th of the on-diagonal biting rates. Panels C, D, G and H show time series for large (C, G) and small primates (D, H) with parameters indicated by the circles in panels A, B, E and F ( and ). The only parameter difference between panels A–D and panels E–H are the off-diagonal biting rates. Contour lines are analytically calculated values of (see Supporting Information S1). The dynamics in the mosquito population are qualitatively identical and can be found in Figure S5. Other parameters are: , , , , , and , .

Figure 5. Example time series of long-period isolations.

This figure indicates the regions of model parameter space that exhibit multiannual dynamics consistent with the observed periodicity of isolations of dengue in Senegal. The blue dots highlight areas of panel A in Figure 4 where the Fourier spectrum has a maximum between 5 and 12 years. The figure also shows an example time series of long-period, synchronized cycles in large primates (panel B) and small primates (panel C). The arrow and green dot indicate the position in parameter space that was used to generate the time series in panels B and C. Here, and are coupled at 1/500th of the on-diagonal biting rates. Contour lines are analytically calculated values of (see Supporting Information S1). The dynamics in the mosquito population are qualitatively identical and can be found in Figure S6. Other parameter values are: , , , , , and , .

Figure 6. Stochastic formulation of the model.

Heatmap of the period of maximum Fourier spectra with corresponding example epidemic time series of prevalence. Panels A, B and C compare transmission probabilities (x-axis) and 1/birth rate (y-axis) for the large primate (panel A) and the small primate (panel B). Birthrates for the small primate are 1/4th of those of the large. Panel A shows periods of oscillations for large primates, B, periods of oscillations for small primates and C the correlation of the mean number of cases in a year (all panels are averaged over 25 runs). D is an example realization of the model with long-periodicity; for both hosts and vectors equal to 0.16 and and 1/17.5 for the large and small primates, respectively. Fourier spectra for the large and small primate time series are shown in panels E and F, respectively. Panels G and H are scatterplots of the number of primate infections versus number of mosquito infections for the large and small primates and their corresponding mosquitoes, respectively. We see transmission dynamics in primates and mosquitoes are highly correlated. The coupling is 1/100 of the on-diagonal biting rates; other parameters are: , , , , , and , , .