Note on a vector-host epidemic model with spatial structure

TL;DR

This paper simplifies the analysis of a vector-host epidemic model with spatial structure, extending previous work by considering different boundary conditions and providing a more straightforward proof of known results.

Contribution

It offers a simplified proof of existing results and explores the model under Dirichlet boundary conditions, expanding the understanding of spatial epidemic dynamics.

Findings

Confirmed the dynamical properties under Neumann boundary conditions

Extended analysis to Dirichlet boundary conditions

Provided a simpler proof of previous results

Abstract

Magal, Webb and Wu [Nonlinearity 31, 5589-5614 (2018)] studied the model describing outbreak of Zika in Rio De Janerio, and provided a complete analysis of dynamical properties for the solutions. In this note we first use a very simple approach to prove their results, and then investigate the modified version of the model concerned in their paper, with Neumann boundary condition replaced by Dirichlet boundary condition.