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

This paper investigates the propagation dynamics of a time-periodic reaction-diffusion SIR epidemic model with vaccination. A key feature of the model is the potential failure of the classical comparison principle, which renders some standard analytical approaches inapplicable. Associated with the basic reproduction number R 0 of the corresponding periodic kinetic system and the spread speed c ∗ , we analyze the spreading properties of the corresponding solution of the system. That is, in case where R 0 > 1 , the disease is persistent behind the front and extinct ahead the front. On this basis, we study the existence and nonexistence of T -periodic traveling wave solutions for the system characterized by R 0 and c ∗ . Finally, numerical simulations further confirm the theoretical predictions. We have found that through the effective implementation of vaccination, the spread of the disease has been significantly slowed.