Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects

Abstract

We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. It is shown that R0 equals the principal eigenvalue of a linear operator associated with a positive eigenfunction. Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. Roughly speaking, if R01, then the endemic steady state is globally attractive under some additional conditions on the incidence rate. Finally, the theoretical results are illustrated by numerical simulations based on a backward Euler method.