Long Period Trajectories of the Seasonal SIR Model

Many infectious diseases exhibit seasonally varying incidence rates. In order to mathematically describe and predict the behavior of such diseases, the seasonal susceptible-infected-removed (Seasonal SIR) model, a system of ordinary differential equations, was formulated. It has been found in numerical simulations of the Seasonal SIR model that sub-harmonic bifurcations may occur, leading to the appearance of periodic modes with inter-outbreak periods on the scale of two time units or more in response to a varying forcing of period one. In the extremes of these long inter-outbreak period modes, it has been observed that periodic modes on the order of nine time units or more may be found. Additionally, these long inter-outbreak period modes exhibit a behaviour of increasing outbreak severity as the time between outbreaks is lengthened. (Continued Within)