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