Periodicity in Epidemiological Models

Various epidemiological mechanisms have been shown to lead to periodic solutions. The most direct way in which periodicity arises is through extrinsic forcing by a parameter such as the contact rate, but periodicity can also arise autonomously. Cyclic models of SIRS or SEIRS type can have periodic solutions if there is a large time delay in the removed class. Epidemiological models with nonlinear incidence of certain general forms can have periodic solutions. Some models with variable population size and disease-related deaths have periodic solutions; most of these are host-parasite models where the parasite lifetime is much shorter than that of the host. Recently, periodic solutions have been found numerically in age structured models with cross immunity between two viral strains.