Epidemic oscillations: Interaction between delays and seasonality

Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly 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 show a general treatment for an SIRS model in which both the infected and the immune phases admit such a description. The general behavior of the system shows transitions between endemic and oscillating situations that could be relevant in many real scenarios. The interaction with the other main source of oscillations, seasonality, is also discussed. This work was presented at the 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL, USA, July 1 5, 2012.