Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment with general nonlinear function

Abstract

We propose a generalization of a model with age of infection in a heterogeneous environment. Firstly, we give the well‐posedness of the model and prove that the solutions are bounded and positive. The difficult mathematical issue in this research is that the model is partially degenerate, and the solution map is not compact. In addition, we construct a global attractor of a bounded set to establish the existence of total trajectory. Moreover, we define the principal eigenvalue associated with a principal eigenvalue problem to give a relation with the basic reproduction number and this value. By assuming that , then the infection‐free steady‐states is globally asymptotically stable. Furthermore, for and by using the persistence results, we prove the existence of endemic steady‐states , and by constructing an appropriate Lyapunov function, we show that is globally asymptotically stable. Lastly, we validate our theoretical analysis by giving some numerical graphics.