This research deals with a spatiotemporal viral infection epidemic model that incorporates double age-dependent susceptibility and infectivity. By using the semigroup theory, we determine the basic reproduction number, denoted as \( {\mathscr {R}}_0 \) , which is identified as the spectral radius of the next-generation operator. Furthermore, we clarify the significance of the threshold represented by \( {\mathscr {R}}_0 \) and examine the impact of the dispersion coefficient \( d \) on \( {\mathscr {R}}_0 \) . The main focus of this paper is to explore the role of \( {\mathscr {R}}_0 \) as a threshold for the global stability of the steady states. Specifically, if \( {\mathscr {R}}_0 < 1 \) , we find that the virus-free steady state is globally asymptotically stable. Conversely, when \( {\mathscr {R}}_0 > 1 \) , it is demonstrated that the solution map remains uniformly persistent, leading to the global asymptotic stability of the positive steady state. The global stability result is obtained with the help of the Lyapunov method on the total trajectory system. Moreover, we examine the effect of a large diffusion rate on the positive steady state, providing valuable insights into how virus mobility influences the final size of the infection.
