Periodic traveling wave of a time periodic and diffusive epidemic model with nonlocal delayed transmission

This work is devoted to the time periodic traveling wave phenomena of a generalization of the classical Kermack–McKendrick model with seasonality and nonlocal interaction derived by mobility of individuals during latent period of disease. When the basic reproduction number R0 is bigger than 1, we find a critical value c∗ and prove the existence of periodic traveling waves with the wave speed c>c∗. When R0 is less than 1, we show that there is no periodic traveling wave with any wave speed c≥0. In addition, the influences of length of latency and seasonal factor on the critical value c∗ is explored by numerical simulations. Some novel epidemiological insights and biological interpretation are provided.