Effect of pathogen-resistant vectors on the transmission dynamics of a vector-borne disease

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

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 R₀ 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 R₀≤1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R₀>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 R₀, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.