Seasonally forced disease dynamics explored as switching between attractors

Biological phenomena offer a rich diversity of problems that can be underst ood using mathematical techniques. Three key features common to many biolog ical systems are temporal forcing, stochasticity and nonlinearity. Here, us ing simple disease models compared to data, we examine how these three fact ors interact to produce a range of complicated dynamics. The study of disea se dynamics has been amongst the most theoretically developed areas of math ematical biology; simple models have been highly successful in explaining t he dynamics of a wide variety of diseases. Models of childhood diseases inc orporate seasonal variation in contact rates due to the increased mixing du ring school terms compared to school holidays. This 'binary' nature of the seasonal forcing results in dynamics that can be explained as switching bet ween two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is f ocused on the behaviour of measles, whooping cough and rubella. (C) 2001 El sevier Science B.V. All rights reserved.