A general multipatch cholera model in periodic environments

This paper is devoted to a general multipatch cholera epidemic model to investigate disease dynamics in a periodic environment. The basic reproduction number \begin{document}$ \mathcal{R}_0 $\end{document} is introduced and a threshold type of result is established in terms of \begin{document}$ \mathcal{R}_0 $\end{document} . Specifically, we show that when \begin{document}$ \mathcal{R}_0<1 $\end{document} , the disease-free steady state is globally attractive if either immigration of hosts is homogeneous or immunity loss of human hosts can be neglected; when \begin{document}$ \mathcal{R}_0>1 $\end{document} , the disease is uniformly persistent and our system admits at least one positive periodic solution. Numerical simulations are carried out to illustrate the impact of asymptotic infections and population dispersal on the spread of cholera. Our result indicates that (a) neglecting asymptotic infections may underestimate the risk of infection; (b) travel can help the disease to become persistent (resp. eradicated) in the network, even though the disease dies out (resp. persists) in each isolated patch.