In this work, we investigate the effects of susceptibility age and infection age on the existence and nonexistence of traveling wave solutions for a diffusive SIR epidemic model. The susceptibility age, denoted by \(a_1\) , represents the time an individual spends in the susceptible class, while the infection age \(a_2\) describes the time elapsed since infection. The model incorporates both age structures into the transmission process, leading to a fully coupled nonlinear system with nonlocal interactions. We establish well-posedness of the model and prove the existence of a minimal wave speed \(c^*\) that characterizes the spatial propagation of the infection. We determine the parameter regimes under which traveling wave solutions exist and show the nonexistence of nontrivial waves for speeds below \(c^*\) . Our results demonstrate that incorporating susceptibility age structure significantly influences wave propagation and can slow or speed up the wave speed, and hence will influence the wave front, thereby affecting the long-term spatial dynamics of disease extinction.
