The role of heterogeneity on the invasion probability of mosquito-borne diseases in multi-host models

Heterogeneity in transmission and stochastic events can play a significant role in shaping the epidemic dynamics of vector-borne infections, especially in the initial phase of an outbreak. In this work, by using multi-type branching process methodologies, we assess how heterogeneities in transmission among a large number of host groups can affect the invasion probabilities of a mosquito-borne disease. We show with both analytical and numerical methods that heterogeneities in transmission can shape the invasion probabilities differently from how they affect the basic reproduction number (R0). In particular, we find that, while R0 always increases with the heterogeneity, the invasion probability after the introduction of infected hosts can decrease with the increase of transmission heterogeneity, even approaching zero when the number of host groups is very large. In addition, we show that the invasion probability via infected vectors is always larger than via infected hosts when heterogeneous transmission is sufficiently high. Our findings suggest that, for multi-species infections (e.g. West Nile fever and Rift Valley fever) or for single-species infections with patchy host distribution, the introduction of primary infected vectors may represent a higher risk for major outbreaks occurrence than introductions of infected hosts