ELSEVIER Preventing Epidemics with Age-Specific Vaccination Schedules NIELS G. BECKER AND ABBAS BAHRAMPOUR School of Statistical Science, La Trobe University, Bundoora, Victoria 3083, Australia Received 29 December 1995; revised 29 October 1996 ABSTRACT A method is proposed for computing the coverage required to prevent epidemics by age-specific vaccination schedules. The method applies in a very general setting and provides explicit expressions in many cases. It can accommodate vaccination doses administered at different ages, heterogeneity among individuals of different ages, a community structured into households, and waning of vaccine-induced immunity. A comparison of results for two specific community settings, with analo- gous parameter values, indicates that the immunity coverage required to prevent epidemics in a community of households is less than that required for a community of uniformly mixing individuals. © Elsevier Science Inc., 1997 1. INTRODUCTION Prevention of epidemics is a major goal of vaccination programs. It is possible to prevent epidemics without immunizing everyone in the community, and there is interest in computing the vaccination coverage required to prevent epidemics. To illustrate, suppose R 0, the basic reproduction number for the spread of an infectious disease in a large community of homogeneous individuals who mix uniformly, is greater than 1. The basic reproduction number is defined as the average number of secondary cases that an initial infective could generate if all others in the community were susceptible. In this simple setting, the critical immunity level v*, which is the immunity coverage above which no epidemics take place, is given by 1 - 1/R o [1-3]. In practice, the demography of the population is dynamic, with new susceptibles being generated by births, and it is useful to consider age-specific vaccination strategies that are able to maintain the immu- nity level above the critical level continuously over time. Here we present a way of computing the vaccination coverage required to prevent epidemics as a function of the age at which the vaccination is administered. Mathematical models have been used previously to inves- MATHEMATICAL BIOSCIENCES 142:63-77 (1997) © Elsevier Science Inc., 1997 655 Avenue of the Americas, New York, NY 10010 0025-5564/97/$17.00 PII S0025-5564(96)00174-5