Mathematical analysis for an age-space structured HIV model with latency

This paper aims to study an HIV model with age structure and latently in a spatially homogeneous environment. By applying the fixed point theorem, we obtain the existence of the global solution and the global attractor for the model. We also identify the explicit formula of the basic reproduction number by the mean of the Laplace transformation, and confirm that this number predicts whether the infection occurs or not. Through analyzing the root distribution of the characteristic equation, the local stability of the equilibrium is obtained. By appealing to the appropriate Lyapunov functionals, we further study the global stability of the equilibrium. Numerical simulations also validate our theoretical results.