Spatial dynamics of an epidemic model in time almost periodic and space periodic media

Abstract

<p style='text-indent:20px;'>This paper is devoted to the study of a reaction-diffusion-advection epidemic model in time almost periodic and space periodic media. First, we obtain a threshold result on the global stability of either zero or the positive time almost periodic solution in terms of the basic reproduction ratio <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Second, we prove the existence of spreading speeds in the partially spatially homogeneous case and the general case. At last, we use numerical simulations to investigate the influence of model parameters on spreading speeds.</p>