The present proposal aims to increase our understanding of childhood diseases including measles, chickenpox, mumps, whooping cough and rubella, all of which exhibit recurrent epidemics. It is proposed, first of all, to better describe the dynamics of the fluctuations through the application of recently developed techniques in nonlinear dynamics. These methods complement traditional time series analysis. In particular, it is hoped to determine if childhood epidemics occur in periodic cycles, with irregularities being due to chance perturbations, or if the dynamics are inherently chaotic, in which case the irregularities would themselves be deterministic. A second major goal is to further elucidate the mechanisms responsible for the outbreaks. Here it is proposed to compare simulated epidemics with actual data using both traditional and nonlinear methods. By comparing several existing models and variants thereto, it is hoped to assess their relative ability to account for the data. Ultimately, this work should lead to improvements in our ability to predict the magnitude and timing of future outbreaks and also the response to variations in public health policy.
