A Study On The Global Asymptomatic Stability Of Two Types Of Viral Models With Density-dependent Diffusion

At present,the study of intercellular virus infection from the dynamic point of view is a hot topic in mathematical and theoretical biology,which is the intersection of mathe-matics and medicine.The establishment of appropriate mathematical models and effective dynamic analysis of the models can be obtained some disease control threshold,which is beneficial to the prevention and treatment of viral disease.In this paper,certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion was in-vestigated.For the virus dynamics model with no time delay,the viral model with a single strain,we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number R₀ and structuring proper Lyapunov functional Moreover,we found that the infection-free equilibrium is globally asymptotically stable if R₀<1,and the infection equilibrium is globally asymptotically stable if R₀>1.For the model with multi-strain,we found that all viral strains coexist if the corresponding basic reproductive number R_j^?>1,while virus will extinct if R_j^?<1.Through research,we find that the virus model with time delay also has these properties.As a result,we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.