A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments

<p style='text-indent:20px;'>In this paper, we propose a reaction-diffusion-advection SIS epidemic model with linear external source to study the effects of open advective environments on the persistence and extinction of infectious diseases. Threshold-type results on the global dynamics in terms of the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_{0} $\end{document}</tex-math></inline-formula> are established. It is found that the introduction of open advective environments leads to different monotonicity and asymptotic properties of the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> with respect to the diffusion rate <inline-formula><tex-math id="M3">\begin{document}$ d_I $\end{document}</tex-math></inline-formula> and advection speed <inline-formula><tex-math id="M4">\begin{document}$ q $\end{document}</tex-math></inline-formula>. Our analytical results suggest that increasing the advection speed or decreasing the diffusion rate of infected individuals helps to eradicate the diseases in open advective environments.</p>