Time series modelling of childhood diseases: a dynamical systems approach

A key issue in the dynamical modelling of epidemics is the synthesis of com plex mathematical models and data by means of time series analysis. We repo rt such an approach, focusing on the particularly well-documented case of m easles. We propose the use of a discrete time epidemic model comprising the infected and susceptible class as state variables. The model uses a discre te time version of the susceptible-exposed-infected-recovered type epidemic models, which can be fitted to observed disease incidence time series. We describe a method for reconstructing the dynamics of the susceptible class, which is an unobserved state variable of the dynamical system. The model p rovides a remarkable fit to the data on case reports of measles in England and Wales from 1944 to 1964. Morever, its systematic part explains the well -documented predominant biennial cyclic pattern. We study the dynamic behav iour of the time series model and show that episodes of annual cyclicity, w hich have not previously been explained quantitatively, arise as a response to a quicker replenishment of the susceptible class during the baby boom, around 1947.