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Discrete time modelling of disease incidence time series by using Markov chain Monte Carlo methods

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  • Alexander Morton
  • Bärbel F. Finkenstädt

Abstract

Summary. A stochastic discrete time version of the susceptible–infected–recovered model for infectious diseases is developed. Disease is transmitted within and between communities when infected and susceptible individuals interact. Markov chain Monte Carlo methods are used to make inference about these unobserved populations and the unknown parameters of interest. The algorithm is designed specifically for modelling time series of reported measles cases although it can be adapted for other infectious diseases with permanent immunity. The application to observed measles incidence series motivates extensions to incorporate age structure as well as spatial epidemic coupling between communities.

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  • Alexander Morton & Bärbel F. Finkenstädt, 2005. "Discrete time modelling of disease incidence time series by using Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 575-594, June.
    • Handle: RePEc:bla:jorssc:v:54:y:2005:i:3:p:575-594
    DOI: 10.1111/j.1467-9876.2005.05366.x
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    Cited by:

    1. Frits Bijleveld & Jacques Commandeur & Phillip Gould & Siem Jan Koopman, 2008. "Model‐based measurement of latent risk in time series with applications," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 265-277, January.
    2. Cici Bauer & Jon Wakefield, 2018. "Stratified space–time infectious disease modelling, with an application to hand, foot and mouth disease in China," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1379-1398, November.
    3. Sifat Sharmin & Md. Israt Rayhan, 2012. "Spatio-temporal modeling of infectious disease dynamics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 875-882, September.
    4. Andrew B Lawson & Joanne Kim, 2021. "Space-time covid-19 Bayesian SIR modeling in South Carolina," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-14, March.

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