Dynamics and asymptotical profiles of an age-structured viral infection model with spatial diffusion

Abstract

In this paper, we propose an age-since-infection virus model with Fickian diffusion and assume that all the parameters depend on the environment. Then we adopt the semigroup theory and the classical renewal process to compute the next generation operator R(x). The basic reproduction R0 is the spectral radius of R(x). Furthermore, we clarify the relationship between R0 and R(x), and investigate asymptotical profile of the basic reproduction number R0 associated with the diffusion rate d. In main part, we show that R0 is a threshold value: the virus-free steady state E0 is globally asymptotically stable if R0<1; otherwise, the endemic steady state E* is globally attractive. Finally, we use backward Euler method to perform some numerical examples to illustrate the theoretical results.