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 \textit{effective} patch-host size. The residence times basic reproduction number ${\mathcal{R}}_0$ 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 ${\mathcal{R}}_0\le 1$ and a unique interior endemic equilibrium is shown to exist that is GAS whenever ${\mathcal{R}}_0>1$ whenever the configuration of host-vector interactions is irreducible. The effects of \textit{patchiness} and \textit{groupness}, a measure of host-vector heterogeneous structure, on the basic reproduction number ${\mathcal{R}}_0$, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.

23 pages and 12 figures

References in corpus (1)

• On the dynamics of a class of multi-group models for vector-borne diseases

Cited by in corpus (5)

• Multi-Patch and Multi-Group Epidemic Models: A New Framework
• Role of short-term dispersal on the dynamics of Zika virus
• Assessing the Efficiency of \textit{Cordon Sanitaire} as a Control Strategy of Ebola
• Can a patchy model describe the potential spread of West Nile virus in Germany?
• Relating Eulerian and Lagrangian spatial models for vector-host diseases dynamics through a fundamental matrix