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Vector-borne diseases models with residence times – A Lagrangian perspective

Abstract:

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts’ dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R<inf>0</inf> is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R<inf>0</inf>≤1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R<inf>0</inf>>1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R<inf>0</inf>, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.