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Estimation in multitype epidemics

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  • T. Britton

Abstract

A multitype epidemic model is analysed assuming proportionate mixing between types. Estimation procedures for the susceptibilities and infectivities are derived for three sets of data: complete data, meaning that the whole epidemic process is observed continuously; the removal processes are observed continuously; only the final state is observed. Under the assumption of a major outbreak in a population of size n it is shown that, for all three data sets, the susceptibility estimators are always efficient, i.e. consistent with a √n rate of convergence. The infectivity estimators are ‘in most cases’ respectively efficient, efficient and unidentifiable. However, if some susceptibilities are equal then the corresponding infectivity estimators are respectively barely consistent (√log(n) rate of convergence), not consistent and unidentifiable. The estimators are applied to simulated data.

Suggested Citation

  • T. Britton, 1998. "Estimation in multitype epidemics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 663-679.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:4:p:663-679
    DOI: 10.1111/1467-9868.00147
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    Cited by:

    1. Huggins, Richard M. & Yip, Paul S. F. & Lau, Eric H. Y., 2004. "A note on the estimation of the initial number of susceptible individuals in the general epidemic model," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 321-330, May.
    2. Demiris, Nikolaos & Kypraios, Theodore & Smith, L. Vanessa, 2012. "On the epidemic of financial crises," MPRA Paper 46693, University Library of Munich, Germany.
    3. Christopher Avery & William Bossert & Adam Clark & Glenn Ellison & Sara Fisher Ellison, 2020. "An Economist's Guide to Epidemiology Models of Infectious Disease," Journal of Economic Perspectives, American Economic Association, vol. 34(4), pages 79-104, Fall.
    4. Yakir Berchenko & Jonathan D. Rosenblatt & Simon D. W. Frost, 2017. "Modeling and analyzing respondent‐driven sampling as a counting process," Biometrics, The International Biometric Society, vol. 73(4), pages 1189-1198, December.
    5. Toshihiko Matsuoka & Tomoki Sato & Tomoyuki Akita & Jiturou Yanagida & Hiroki Ohge & Masao Kuwabara & Junko Tanaka, 2016. "High Vaccination Coverage among Children during Influenza A(H1N1)pdm09 as a Potential Factor of Herd Immunity," IJERPH, MDPI, vol. 13(10), pages 1-17, October.

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