Epidemic models with uncertainty in the reproduction number.

Journal of Mathematical Biology
M G Roberts

Abstract

One of the first quantities to be estimated at the start of an epidemic is the basic reproduction number, R₀. The progress of an epidemic is sensitive to the value of R₀, hence we need methods for exploring the consequences of uncertainty in the estimate. We begin with an analysis of the SIR model, with R₀ specified by a probability distribution instead of a single value. We derive probability distributions for the prevalence and incidence of infection during the initial exponential phase, the peaks in prevalence and incidence and their timing, and the final size of the epidemic. Then, by expanding the state variables in orthogonal polynomials in uncertainty space, we construct a set of deterministic equations for the distribution of the solution throughout the time-course of the epidemic. The resulting dynamical system need only be solved once to produce a deterministic stochastic solution. The method is illustrated with R₀ specified by uniform, beta and normal distributions. We then apply the method to data from the New Zealand epidemic of H1N1 influenza in 2009. We apply the polynomial expansion method to a Kermack-McKendrick model, to simulate a forecasting system that could be used in real time. The results demonstrate the...Continue Reading

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Citations

Apr 27, 2013·Bulletin of Mathematical Biology·J R Artalejo, M J Lopez-Herrero
Apr 10, 2014·PloS One·Jean-Paul ChretienF Ellis McKenzie
Jan 22, 2014·Journal of Theoretical Biology·R I Hickson, M G Roberts
Aug 5, 2015·Journal of Invertebrate Pathology·Eric N Powell, Eileen E Hofmann
Apr 20, 2016·Mathematical Biosciences·David B Harman, Peter R Johnston
Aug 16, 2016·Mathematical Biosciences·M G Roberts
Sep 15, 2016·Physical Review. E·Menachem Lachiany, Yoram Louzoun
Oct 5, 2018·BMC Medicine·Kathleen M O'ReillyLaith Yakob
May 24, 2021·Journal of Mathematical Biology·Giacomo AlbiMattia Zanella
Jun 27, 2021·Journal of Mathematical Biology·G DimarcoM Zanella
Jul 3, 2021·Mathematical Biosciences and Engineering : MBE·Mattia ZanellaGiuseppe Toscani
Aug 29, 2021·Journal of Biomedical Informatics·Liang LiBiqing Huang
Nov 25, 2021·Mathematical Biosciences and Engineering : MBE·Giacomo AlbiMattia Zanella

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