An infection age-space-structured SIR epidemic model with Dirichlet boundary condition

In this paper, we are concerned with the global asymptotic behavior of an SIR epidemic model with infection age-space structure. Under the homogeneous Dirichlet boundary condition, we first reformulate the model into the coupled reaction-diffusion and difference system by using the method of characteristics. We then obtain the spatially heterogeneous disease-free steady state and define the basic reproduction number ℛ 0 by the spectral radius of the next generation operator. We then show the existence and uniqueness of the global classical solution by constructing suitable upper and lower solutions. As a threshold result, we establish that the disease-free steady state is globally attractive if ℛ 0 < 1, whereas the system is uniformly weakly persistent in norm if ℛ 0 > 1. Finally, numerical simulations are exhibited to illustrate our theoretical results together with how to compute ℛ 0 .