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Estimating the Basic Reproductive Number in the General Epidemic Model with an Unknown Initial Number of Susceptible Individuals

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  • ERIC H. Y. LAU
  • PAUL S. F. YIP

Abstract

. In any epidemic, there may exist an unidentified subpopulation which might be naturally immune or isolated and who will not be involved in the transmission of the disease. Estimation of key parameters, for example, the basic reproductive number, without accounting for this possibility would underestimate the severity of the epidemics. Here, we propose a procedure to estimate the basic reproductive number (R0) in an epidemic model with an unknown initial number of susceptibles. The infection process is usually not completely observed, but is reconstructed by a kernel‐smoothing method under a counting process framework. Simulation is used to evaluate the performance of the estimators for major epidemics. We illustrate the procedure using the Abakaliki smallpox data.

Suggested Citation

  • Eric H. Y. Lau & Paul S. F. Yip, 2008. "Estimating the Basic Reproductive Number in the General Epidemic Model with an Unknown Initial Number of Susceptible Individuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 650-663, December.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:4:p:650-663
    DOI: 10.1111/j.1467-9469.2008.00594.x
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Schimit, P.H.T. & Monteiro, L.H.A., 2012. "On estimating the basic reproduction number in distinct stages of a contagious disease spreading," Ecological Modelling, Elsevier, vol. 240(C), pages 156-160.

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