Dynamics of a Spatiotemporal Viral Infection Model with Two Age Structures and Nonlinear Incidence Function

This study investigates a spatiotemporal model for the spread of a viral infection, which incorporates two different types of ages, susceptibility age [Formula: see text], and infection age [Formula: see text], and spatial heterogeneity of the environment. The investigated model considers a generalized nonlinear incidence function that introduces additional complexity to the disease dynamics. By employing the theory of semigroups, we identify the basic reproduction number [Formula: see text], which is characterized as the spectral radius of the next-generation operator. We further identify the sensitivity of this number with respect to the dispersion coefficient [Formula: see text]. The principal aim is to investigate the global dynamics governed by [Formula: see text], and spotlighting the mathematical challenges obtained by considering both, the nonlinear incidence function, and the susceptible age dependent. Indeed, when [Formula: see text], it is obtained that the virus-free steady state is globally asymptotically stable. In contrast, if [Formula: see text], the solution map is proven to be uniformly persistent, and the positive steady state becomes globally asymptotically stable. These results are established through the application of Lyapunov functionals applied to the total trajectories system. Additionally, we explore the asymptotic profiles of the positive steady state for large dispersion rates, shedding light on the effect of large diffusion rate of the positive steady state.