Transients and attractors in epidemics.
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.
Bauch
Chris T
CT
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada. bauch@math.mcmaster.ca
Earn
David J D
DJ
D002648:Child; D003141:Communicable Diseases / Q000453:epidemiology*; D003710:Demography; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D005583:Fourier Analysis; D006801:Humans; D012621:Seasons; D013269:Stochastic Processes