On a reaction-diffusion virus model with general boundary conditions in heterogeneous environments

TL;DR

This paper develops a reaction-diffusion model with general boundary conditions to study the spread of West Nile and Zika viruses in heterogeneous environments, establishing conditions for persistence and stability of the disease.

Contribution

It introduces a novel time-periodic reaction-diffusion model with general boundary conditions for virus propagation in heterogeneous settings, proving existence, uniqueness, and stability of solutions.

Findings

Positive time periodic solutions exist if and only if the basic reproduction ratio exceeds one.

The positive solutions are unique and globally asymptotically stable when they exist.

The model captures the effects of heterogeneity and boundary conditions on virus persistence.

Abstract

To describe the propagation of West Nile virus and/or Zika virus, in this paper, we propose and study a time-periodic reaction-diffusion model with general boundary conditions in heterogeneous environments and with four unknowns: susceptible host, infectious host, susceptible vector and infectious vector. We can prove that such problem has a positive time periodic solution if and only if host and vector persist and the basic reproduction ratio is greater than one, and moreover the positive time periodic solution is unique and globally asymptotically stable when it exists.