Mathematical Modeling of Age-Structured Viral Infections: Integrating Virus-to-Cell and Direct Cell Transmission

Viral infection dynamics are influenced by both the maturation age of viral particles and multiple transmission pathways. We develop a novel age-structured PDE model that unifies virus-to-cell and direct cell-to-cell transmission, tracking viral density as a function of infection age with general nonlinear incidence. We establish well-posedness and the existence of a global compact attractor. The explicit basic reproduction number R₀ acts as a sharp threshold: if R₀<1, the infection-free equilibrium is globally asymptotically stable; if R₀>1, a unique infected steady state exists and is shown to be globally stable under a proportionality condition on the incidence functions. This is proven by constructing a Lyapunov functional and employing persistence theory. Our framework elucidates how age structure and dual transmission routes jointly determine infection outcomes, providing a theoretical basis for assessing strategies aimed at disrupting viral persistence, such as vaccines or antiviral therapies.