Noise and Nonlinearity in Epidemics : combining statistical and mechanistic modeling to characterize and forecast population dynamics

Childhood disease epidemics in large cities, notably measles, have been proposed as a well-supported example of deterministic chaos underlying complex population dynamics, but this remains controversial. Methods based on nonlinear time series modeling identify these epidemics as nonlinear with substantial random noise, clustering near the transition between stability and chaos. This conclusion has been challenged on the ground that the time series models have lower forecasting accuracy than mechanistic models with chaotic dynamics. However, the time series models in this comparison were all linear. Here we broaden the comparison to include nonlinear time series models for the "noisy nonlinearity" hypothesis, introducing an intermediate class of "semi-mechanistic" models which incorporate some mechanistic structure while retaining statistical flexibility. All of the nonlinear time series models exhibited higher prediction accuracy than deterministic chaotic models, but the semi-mechanistic model was by far the most accurate. This comparsion suggests that for forecasting, control, and other practical applications on populations other than measles, semi-mechanistic modeling may be the most effective approach for characterizing and predicting population dynamics from limited data. Characterization of measles dynamics based on the semi-mechanistic models indicates that the dynamics have an appreciable random component, are near the border between stability and chaos, and vary between local (in state space) stability and chaos.