Dynamics of virus infection models with density-dependent diffusion

Density-dependent diffusion plays an important role in the process of viral infection. In this paper, we construct mathematical models to investigate the dynamics of the viruses and their control. Single strain and multi-strain viral infections are both considered in this work. Using the method proposed by Pao and Ruan (2013), we prove the well-posedness of the models. By constructing appropriate Lyapunov functions, we proved the global asymptotical stabilities of the models. For the multi-strain model, we show that when the basic reproduction number for each strain is greater than one, all viral strains coexist. Since the effect of different treatments may result in competitive exclusion, it is essential to employ the treatment with combined therapy. We find with surprise that the density-dependent diffusion of the virus does not influence the global stabilities of the model with homogeneous Neumann boundary conditions.