Publication: Transients and attractors in epidemics

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Title	Transients and attractors in epidemics
Authors/Editors*	C. T. Bauch, D. J. D. Earn
Where published*	Proceedings of the Royal Society of London, Series B
How published*	Journal
Year*	2003
Volume	270
Number	1524
Pages	1573-1578
Publisher	The Royal Society
Keywords	childhood disease dynamics; seasonal forcing, SEIR model; perturbation theory; demographic stochasticity; Poincare map
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Abstract	Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.