Abstract
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 numberℛ0by 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 ifℛ0< 1, whereas the system is uniformly weakly persistent in norm ifℛ0> 1. Finally, numerical simulations are exhibited to illustrate our theoretical results together with how to computeℛ0.
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