A periodic age-structured epidemic model with a wide class of incidence rates

In this paper, a time-delayed epidemic model is formulated to describe the dynamics of seasonal diseases with age structure. By the method of the spectral radius of an integral operator, we define the basic reproduction number ( R 0 ) of the model. It is shown that the disease is uniformly persistent and there exists at least one positive periodic state when R 0 > 1 while the disease will die out if R 0 < 1 . The presented case study not only confirms the theoretical results, but also demonstrates that the epidemic peak is very sensitive to the maturation period and the magnitude of seasonality, which is different from the dynamics of the model without considering age heterogeneities. These findings contribute to better understanding the epidemiological properties of the disease with age structure.