WKB calculation of an epidemic outbreak distribution

Andrew J. Black, Alan J. McKane

    Research output: Contribution to journalArticlepeer-review


    We calculate both the exponential and prefactor contributions in a WKB approximation of the master equation for a stochastic SIR model with highly oscillatory dynamics. Fixing the basic parameters of the model, we investigate how the outbreak distribution changes with the population size. We show that this distribution rapidly becomes highly non-Gaussian, acquiring large tails, indicating the presence of rare but large outbreaks, as the population is made smaller. The analytic results are found to be in excellent agreement with simulations until the systems become so small that the dynamics are dominated by fade-out of the disease. © 2011 IOP Publishing Ltd and SISSA.
    Original languageEnglish
    Article numberP12006
    JournalJournal of Statistical Mechanics: Theory and Experiment
    Issue number12
    Publication statusPublished - Dec 2011


    • epidemic modelling
    • stochastic processes (theory)


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