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

摘要

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 semi-group theory and the classical renewal process to compute the next generation operator R(x). The basic reproduction R-0 is the spectral radius of R(x). Furthermore, we clarify the relationship between R-0 and R(x), and investigate asymptotical profile of the basic reproduction number R-0 associated with the diffusion rate d. In main part, we show that R-0 is a threshold value: the virus-free steady state E-0 is globally asymptotically stable if R-0 < 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. (C) 2019 Elsevier Inc. All rights reserved.