A time since recovery model with varying rates of loss of immunity

pre-printFor many infectious diseases, immunity wanes over time. The majority of SIRS models assume that this loss of immunity takes place at a constant rate. We study temporary immunity within a SIRS model structure if the rate of loss of immunity can depend on the time since recovery from disease.We determine the conditions under which the endemic steady state becomes unstable and periodic oscillations set in, showing that a fairly rapid change between slow and rapid immunity loss is necessary to produce oscillations