Chance and Chaos in Measles Dynamics

SUMMARY This paper examines the impact of seasonality and chaotic dynamics in simple models for the population dynamics of measles on the probability of fade-out of infection. It uses Monte Carlo simulations of the seasonally forced SEIR model, with parameters appropriate to a city of 1 million people. The incidence of fade-out in a spatially homogeneous model is compared with simple spatial models involving various degrees of coupling between subareas. The results indicate a significant degree of fade-out of infection, which is not consistent with previously derived criteria for the persistence of measles. Lowering the degree of spatial coupling does not substantially reduce the extent of fade-out. A simple non-linear analysis of the simulated series is presented, and the epidemiological implications of these results are discussed.