Sufficient conditions for global dynamics of a viral infection model with nonlinear diffusion

Abstract

In this paper, we study the global dynamics of a viral infection model with spatial heterogeneity and nonlinear diffusion. For the spatially heterogeneous case, we first derive some properties of the basic reproduction number \begin{document}$ R_0 $\end{document} . Then for the auxiliary system with quasilinear diffusion, we establish the comparison principle under some appropriate conditions. Some sufficient conditions are derived to ensure the global stability of the virus-free steady state. We also show the existence of the positive non-constant steady state and the persistence of virus. For the spatially homogeneous case, we show that \begin{document}$ R_0 $\end{document} is the only determinant of the global dynamics when the derivative of the function \begin{document}$ g $\end{document} with respect to \begin{document}$ V $\end{document} (the rate of change of infected cells for the repulsion effect) is small enough. Our simulation results reveal that pyroptosis and Beddington-DeAngelis functional response function play a crucial role in the controlling of the spreading speed of virus, which are some new phenomena not presented in the existing literature.