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

Abstract 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 R 0 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 R 0 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.