Estimating variability in models for recurrent epidemics: assessing the use of moment closure techniques

The major role played by demographic stochasticity in determining the dynamics and persistence of childhood diseases, such as measles, chickenpox and pertussis, has long been realized. Techniques which can be used to estimate the magnitude of this stochastic effect are of clear importance. In this study, we assess and compare the use of two moment closure approximations to estimate the variability seen about the average behavior of stochastic models for the recurrent epidemics seen in childhood diseases. The performance of the approximations are assessed using analytic techniques available for the simplest epidemiological model and using numerical simulations in more complex settings. We also present epidemiologically important extensions of previous work, considering variability in the SEIR model and in situations for which there is seasonal variation in disease transmission. Important implications of stochastic effects for the dynamics of childhood diseases are highlighted, including serious deficiencies of deterministic descriptions of dynamical behavior.