Stochastic amplification in epidemics

David Alonso, Alan J. McKane, Mercedes Pascual

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The role of stochasticity and its interplay with nonlinearity are central current issues in studies of the complex population patterns observed in nature, including the pronounced oscillations of wildlife and infectious diseases. The dynamics of childhood diseases have provided influential case studies to develop and test mathematical models with practical application to epidemiology, but are also of general relevance to the central question of whether simple nonlinear systems can explain and predict the complex temporal and spatial patterns observed in nature outside laboratory conditions. Here, we present a stochastic theory for the major dynamical transitions in epidemics from regular to irregular cycles, which relies on the discrete nature of disease transmission and low spatial coupling. The full spectrum of stochastic fluctuations is derived analytically to show how the amplification of noise varies across these transitions. The changes in noise amplification and coherence appear robust to seasonal forcing, questioning the role of seasonality and its interplay with deterministic components of epidemiological models. Childhood diseases are shown to fall into regions of parameter space of high noise amplification. This type of 'endogenous' stochastic resonance may be relevant to population oscillations in nonlinear ecological systems in general. © 2006 The Royal Society.
    Original languageEnglish
    Pages (from-to)575-582
    Number of pages7
    JournalJournal of the Royal Society Interface
    Volume4
    Issue number14
    DOIs
    Publication statusPublished - 22 Jun 2007

    Keywords

    • Childhood diseases
    • Endogenous stochastic resonance
    • Epidemics
    • Oscillations
    • Stochastic modelling

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