Disease transmission dynamics of an epidemiological predator-prey system in open advective environments

Abstract

<p style='text-indent:20px;'>This paper delves into the dynamics of a spatial eco-epidemiological system with disease spread within the predator population in open advective environments. The disease-free subsystem is first discussed, and the net reproductive rate <inline-formula><tex-math id="M1">\begin{document}$ R_P $\end{document}</tex-math></inline-formula> is established to determine whether the predator can invade successfully. The impacts of advection rate on <inline-formula><tex-math id="M2">\begin{document}$ R_P $\end{document}</tex-math></inline-formula> are also discussed. Then for the scenario of successful invasion of the predator, sufficient conditions for the prevalence of disease and the local stability of disease-free attractor are obtained by dint of persistence theory and comparison theorem. Finally, we present a special numerical example, in which the basic reproduction ratio <inline-formula><tex-math id="M3">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> of the disease is established in the absence or presence of periodic perturbation. Our theoretical and numerical results both indicate that the advection rate in an intermediate interval can favor the coexistence of prey and healthy predator as well as the eradication of disease.</p>