Spreading and vanishing in a West Nile virus model with expanding fronts

TL;DR

This paper analyzes a spatial West Nile virus model with a free boundary, identifying conditions for virus spread or eradication, and demonstrating how initial infection levels, bird diffusion, and habitat size influence outcomes.

Contribution

It introduces a coupled PDE-ODE free boundary model for WNv spread, providing new criteria for virus vanishing or spreading based on model parameters.

Findings

Initial infected populations significantly affect virus spread.

Higher bird diffusion rates promote virus spreading.

Larger initial habitats increase the likelihood of virus persistence.

Abstract

In this paper, we study a simplified version of a West Nile virus model discussed by Lewis et al. [28], which was considered as a first approximation for the spatial spread of WNv. The basic reproduction number $R_0$ for the non-spatial epidemic model is defined and a threshold parameter $R_0 ^D$ for the corresponding problem with null Dirichlet boundary condition is introduced. We consider a free boundary problem with coupled system, which describes the diffusion of birds by a PDE and the movement of mosquitoes by a ODE. The risk index $R_0^F (t)$ associated with the disease in spatial setting is represented. Sufficient conditions for the WNv to eradicate or to spread are given. The asymptotic behavior of the solution to system when the spreading occurs are considered. It is shown that the initial number of infected populations, the diffusion rate of birds and the length of initial habitat exhibit important impacts on the vanishing or spreading of the virus. Numerical simulations are presented to illustrate the analytical results.