Threshold Dynamics for Infection Age-Structured Epidemic Models with Spatial Diffusion and Degenerate Diffusion

This paper is devoted to studying the threshold dynamics for infection age-structured epidemic models with non-degenerate diffusion and degenerate diffusion. For general infection age-structured epidemic models with non-degenerate diffusion, we establish the basic reproduction number R-0 by using non-densely defined operators and prove that R-0 equals the spectral radius of -FA(-1). For a class of infection age-structured epidemic models with non-degenerate diffusion or degenerate diffusion, we give a general method to prove that R-0 plays the role of the threshold for the extinction or persistence of the disease. Finally, we apply our methods to the infection age-structured SIR, SEIR epidemic models and obtain the threshold results on their global dynamics. Our results on R-0 for the general infection age-structured epidemic models extend the cases of ODE and reaction-diffusion epidemic models. In addition, our method in this paper improves some previous results and is applicable to the Neumann, Dirichlet, and Robin boundary conditions.