Biostatistics (2003), 4, 4, pp. 621–632 Printed in Great Britain
Estimation of effective reproduction numbers for infectious diseases using serological survey data C. P. FARRINGTON∗ , H. J. WHITAKER Department of Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
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S UMMARY The effective reproduction number of an infection, denoted Re , may be used to monitor the impact of a vaccination programme. If Re is maintained below 1, then sustained endemic transmission of the infection cannot occur. In this paper we discuss methods for estimating Re from serological survey data, allowing for age and individual heterogeneity. We describe semi-parametric and parametric models, and obtain an upper bound on Re when vaccine coverage and efficacy are not known. The methods are illustrated using data on mumps and rubella in England and Wales. Keywords: Eigenvalue; Frailty; Infectious disease; Reproduction number; Vaccine.
1. I NTRODUCTION Mass vaccination programmes against common childhood infections aim both to protect the individuals vaccinated, and to control the spread of infection in the population. The phenomenon of herd immunity makes it possible to eliminate an infection even though not all individuals are vaccinated. Elimination means reducing the number of susceptibles below a critical threshold, so that spread from an infective cannot produce a large epidemic. Whether a vaccination programme is achieving elimination at a particular time t after the introduction of mass vaccination is determined by the effective reproduction number of the infection at time t. This quantity, denoted Re (t), is the average number of infectious individuals resulting from a single infective introduced at time t into the popul