Propagation Dynamics of a time-periodic reaction-diffusion SIR epidemic model with vaccination

This paper investigates propagation dynamics of a time-periodic reaction-diffusion SIR epidemic model with vaccination, which is not applicable to the classical comparison principle. Firstly, we characterize the transmission behavior of this system in terms of the basic reproduction number R 0 and the minimal spreading speed c * , both derived from the corresponding periodic kinetic system. Specifically, if R 0 > 1, the disease persists behind the propagating fronts moving with speed 0 c * . On this basis, we further study the existence and non-existence of T-periodic traveling wave solutions for this system. Finally, these theoretical results are illustrated by numerical simulations, and the explicit expressions of R 0 and c * reveal that increasing vaccination coverage can effectively delay the spread of the disease.