Assuming total population remains constant, this paper establishes a class of MSIR epidemic models with both natural age and infection-age and studies the stability of the equilibrium solutions of this model. Firstly, by normalizing the model and linearizing it at the disease-free equilibrium, demonstrating that when R₁<1, the disease-free equilibrium is locally asymptotically stable. Subsequently, employing the method of characteristics for hyperbolic systems and Fatou's lemma, it is proven that when R₁<1, the disease-free equilibrium is globally asymptotically stable. Finally, the existence of a unique endemic equilibrium solution is established using the intermediate value theorem when R₁>1.