The effect of random vaccine response on the vaccination coverage requiredto prevent epidemics

The response people have to vaccination varies because their immune systems differ and vaccine failures occur. Here we consider the effect that a rand om response, independent for each vaccinee, has on the vaccination coverage required to prevent epidemics in a large community. For a community of uni formly mixing individuals an explicit expression is found for the critical vaccination coverage (CVC) and the effect of the vaccine response is determ ined entirely by the mean E(AB), where A and B, respectively, reflect the i nfectivity and susceptibility of a vaccinated individual. This result shows that the usual concept of vaccine efficacy, which focuses on the amount of protection the vaccine provides the vaccinee against infection, is not ade quate to describe the requirements for preventing epidemics when vaccinatio n affects infectivity. The estimation of E(AB) poses a problem because A an d B refer to the vaccine response of the same individual. Similar results a re found when there are different types of individual, but now the mean E(A B) may differ between types. However, for a community made up of households it is shown that the CVC also depends on other characteristics of the vacc ine response distribution. In practice this means that estimating a single measure of vaccine effectiveness is generally not enough to determine the C VC. For a specific community of households it is found that the vaccination coverage required to prevent epidemics decreases as the variation in the v accine response increases. (C) 1998 Elsevier Science Inc. All rights reserv ed.