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

Abstract EN

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 R0<1, then the virus-free steady state is globally asymptotically stable; if R0>1, 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.