Abstract
Observational studies indicate that vaccine-induced immunity can decline over time. However, few researchers have incorporated this kind of waning effect into their virus spread models. In this study, we simulate an influenza epidemic that considers the effects of waning immunity by fitting epidemiological models to CDC secondary historical data aggregated on a weekly basis, and derive the transmission rates at which susceptible individuals become infected over the course of the influenza season. Using a system of differential equations, we define four groups of individuals in a population: susceptible, vaccinated, infected, and recovered. We show that a larger number of initially infected individuals might not only bring the influenza season to an end sooner but also reduce the epidemic size. Moreover, any influenza virus that entails a faster recovery rate does not necessarily lead to a smaller epidemic size. We illustrate how simulation helps in understanding the effects of influenza epidemiological model in the presence of waning influenza vaccine immunity.