NOISE AND NONLINEARITY IN MEASLES EPIDEMICS - COMBINING MECHANISTIC AND STATISTICAL APPROACHES TO POPULATION MODELING

We present and evaluate an approach to analyzing population dynamics d ata using semimechanistic models. These models incorporate reliable in formation on population structure and underlying dynamic mechanisms bu t use nonparametric surface-fitting methods to avoid unsupported assum ptions about the precise form of rate equations. Using historical data on measles epidemics as a case study, we show how this approach can l ead to better forecasts, better characterizations of the dynamics, and a better understanding of the factors causing complex population dyna mics relative to either mechanistic models or purely descriptive stati stical time-series models. The semimechanistic models are found to hav e better forecasting accuracy than either of the model types used in p revious analyses when tested on data not used to fit the models. The d ynamics are characterized as being both nonlinear and noisy, and the g lobal dynamics are clustered very tightly near the border of stability (dominant Lyapunov exponent lambda approximate to 0). However, locall y in state space the dynamics oscillate between strong short-term stab ility and strong short-term chaos (i.e., between negative and positive local Lyapunov exponents). There is statistically significant evidenc e for short-term chaos in all data sets examined. Thus the nonlinearit y in these systems is characterized by the variance over state space i n local measures of chaos versus stability rather than a single summar y measure of the overall dynamics as either chaotic or nonchaotic.