Vector borne diseases on an urban environment: The effects of heterogeneity and human circulation

We study the effect of human circulation and host/vector heterogeneities on the onset of epidemics of arboviruses. From a meta-population dynamics based on the classical Bailey–Dietz model, we derive a multi-group model under three assumptions: (i) fast host sojourn time-scale; (ii) mosquitoes do not move; (iii) time homogeneity and strong connectivity of human circulation. Within this modelling framework, three different kinds of R₀ appear: (i) the “true” or “global” R₀—derived from the corresponding next generation matrix; (ii) the uniform R₀—obtained if the patches are taken homogeneous; (iii) the local R₀s—obtained if the patches are disconnected. We show that there is relevant epidemiological information associated to all of them. In particular, they can be used to understand the effects of changing the circulation on the value of the global R₀. We also present additional results on the effects on R₀ of different vector control policies, and a simulation with data from the city of Rio de Janeiro, Brazil.