Global dynamics of a time-delayed nonlocal reaction-diffusion model of within-host viral infections

Abstract

In this paper, we study a time-delayed nonlocal reaction-diffusion model of within-host viral infections. We introduce the basic reproduction number $R_0$ and show that the infection-free steady state is globally asymptotically stable when $R_0\le 1$ , while the disease is uniformly persistent when $R_0>1$ . In the case where all coefficients and reaction terms are spatially homogeneous, we obtain an explicit formula of $R_0$ and the global attractivity of the positive constant steady state. Numerically, we illustrate the analytical results, conduct sensitivity analysis, and investigate the impact of drugs on curtailing the spread of the viruses.

Keywords: Non-local infections; Threshold dynamics; Time delay; Within-host dynamics.