Threshold Dynamics and Competitive Exclusion in a Virus Infection Model with General Incidence Function and Density-Dependent Diffusion

Abstract

In this paper, we investigate single-strain and multistrain viral infection models with general incidence function and density-dependent diffusion subject to the homogeneous Neumann boundary conditions. For the single-strain viral infection model, by using the linearization method and constructing appropriate Lyapunov functionals, we obtain that the global threshold dynamics of the model is determined by the reproductive numbers for viral infection ℛ0. For the multistrain viral infection model, we have discussed the competitive exclusion problem. If the reproduction number ℛi for strain i is maximal and larger than one, the steady state Ei corresponding to the strain i is globally stable. Thus, competitive exclusion happens and all other strains die out except strain i. Meanwhile, we can prove that the single-strain and multistrain viral infection models are well posed. Furthermore, numerical simulations are also carried out to illustrate the theoretical results, which is seldom seen in the relevant known literatures.