Synchrony of Sylvatic Dengue Isolations: A Multi-Host, Multi-Vector SIR Model of Dengue Virus Transmission in Senegal

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.