Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model

Abstract

<p style='text-indent:20px;'>Taking account of spatial heterogeneity, latency in infected individuals, and time for shed bacteria to the aquatic environment, we build a delayed nonlocal reaction-diffusion cholera model. A feature of this model is that the incidences are of general nonlinear forms. By using the theories of monotone dynamical systems and uniform persistence, we obtain a threshold dynamics determined by the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal {R}_0 $\end{document}</tex-math></inline-formula>. Roughly speaking, the cholera will die out if <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0&lt;1 $\end{document}</tex-math></inline-formula> while it persists if <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{R}_0&gt;1 $\end{document}</tex-math></inline-formula>. Moreover, we derive the explicit formulae of <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> for two concrete situations.