Revisited measles and chickenpox dynamics through orthogonal transformation

The question addressed is whether or not childhood epidemics such as measle s and chickenpox are characterized by low-dimensional chaos. We propose a n ew method for the detection and extraction of hidden periodic components em bedded in an irregular cyclical series, and study the characterization of t he epidemiological series in terms of the characteristic features or period icity attributes of the extracted components. It is shown that the measles series possesses two periodic components each having a period of one year. Both the periodic components have time-varying pattern, and the process is nonlinear and deterministic; there is no evidence of strong chaoticity in t he measles dynamics. The chickenpox series has one seasonal component with stable pattern, and the process is deterministic but linear, and hence non- chaotic. We also propose surrogate generators based on null hypotheses rela ting to the variability of the periodicity attributes to analyse the dynami cs in the epidemic series. The process dynamics is also studied using seaso nally forced SEIR epidemic model, and the characterization performance of t he proposed schemes is assessed. (C) 1999 Academic Press.