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Biostatistics 1:389-402 (2000)
© 2000 Oxford University Press

Estimating the immunity coverage required to prevent epidemics in a community of households

Tom Britton1,* and Niels G. Becker2

1 Department of Mathematics, Uppsala University, , S-751 06, Uppsala, Swedentom.britton{at}math.uu.se
2 National Centre for Epidemiology and Population Health, Australian National University, Canberra ACT 0200, Australia

An estimation of the immunity coverage needed to prevent future outbreaks of an infectious disease is considered for a community of households. Data on outbreak size in a sample of households from one epidemic are used to derive maximum likelihood estimates and confidence bounds for parameters of a stochastic model for disease transmission in a community of households. These parameter estimates induce estimates and confidence bounds for the basic reproduction number and the critical immunity coverage, which are the parameters of main interest when aiming at preventing major outbreaks in the future. The case when individuals are homogeneous, apart from the size of their household, is considered in detail. The generalization to the case with variable infectivity, susceptibility and/or mixing behaviour is discussed more briefly. The methods are illustrated with an application to data on influenza in Tecumseh, Michigan.

Keywords: Basic reproduction number; Disease transmission; Epidemic data; Herd immunity; Household community; Household outbreaks; Infection parameters; Maximum likelihood estimation; Preventing epidemics; Stochastic epidemic model; Vaccination coverage


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