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

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.

[1]  I. Longini,et al.  Tecumseh study of illness. XIII. Influenza infection and disease, 1976-1981. , 1985, American journal of epidemiology.

[2]  N G Becker,et al.  The effect of random vaccine response on the vaccination coverage required to prevent epidemics. , 1998, Mathematical biosciences.

[3]  N G Becker,et al.  Preventing epidemics in a community of households. , 1996, Epidemiology and infection.

[4]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[5]  A. Langworthy,et al.  An influenza simulation model for immunization studies. , 1976, American journal of epidemiology.

[6]  D. Balding,et al.  Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods , 2000 .

[7]  Klaus Dietz,et al.  Reproduction Numbers and Critical Immunity Levels for Epidemics in a Community of Households , 1996 .

[8]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[9]  N. L. Johnson,et al.  Linear Statistical Inference and Its Applications , 1966 .

[10]  T. Britton.  On critical vaccination coverage in multitype epidemics , 1998, Journal of Applied Probability.

[11]  N G Becker,et al.  Immunization levels for preventing epidemics in a community of households made up of individuals of various types. , 1996, Mathematical biosciences.

[12]  S. Utev,et al.  The effect of community structure on the immunity coverage required to prevent epidemics. , 1998, Mathematical biosciences.

[13]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[14]  F. Ball,et al.  Epidemics with two levels of mixing , 1997 .

[15]  I. Longini,et al.  A generalized stochastic model for the analysis of infectious disease final size data. , 1991, Biometrics.

[16]  T. Britton,et al.  Statistical studies of infectious disease incidence , 1999 .