Note on a vector-host epidemic model with spatial structure

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.