Global Dynamics of a Nonlocal Delayed Viral Infection Model in Heterogeneous Environments

Abstract

This work is devoted to the mathematical analysis of within-host viral infection dynamics, with particular emphasis on the hepatitis B virus. We first review three classical models that progressively incorporate spatial structure: the foundational ODE model of Nowak et al [23], the local diffusion model of Wang and Wang [29], and the nonlocal dispersal frame- work of Wang et al [30]. We then conduct a rigorous study of the spatially heterogeneous model proposed by Liu et al [17], which simultaneously incorporates nonlocal diffusion of free virions governed by a probability kernel J, an intracellular delay τ > 0 reflecting the latency between viral entry and viral production, and position-dependent biological parameters. The analysis is carried out in an infinite-dimensional functional framework. We establish the global well-posedness and positivity of solutions via semigroup theory and the Banach fixed point theorem, and prove that the semiflow is bounded dissipative. Asymptotic smoothness of the semiflow and the existence of a compact global attractor are obtained through a Kuratowski measure argument. Finally, the global asymptotic stability of the infection-free steady state P0 is established when R0 ≤ 1, via an explicit Lyapunov functional whose integral kernel is the positive eigenfunction of the linearised problem around P0.