Epidemic oscillations: Interaction between delays and seasonality

Abstract

Traditional epidemic models consider that individual processes occur at constant rates; an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption indeed fails for almost all infectious diseases, in which the infection time usually follows a probability distribution more or less spread around a mean value. We presented some years ago a general treatment for an SIRS model in which both the infected and the immune phases admit such a description, where the system shows transitions between endemic and oscillating situations. In the present contribution, we consider the effect of seasonality on the transmission rate. Performing numerical simulations of the delayed equations plus seasonality, we have found a rich and complex scenario of oscillations that could be relevant in real epidemics.