The effect of random vaccine response on the vaccination coverage required to 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 random response, independent for each vaccinee, has on the vaccination coverage required to prevent epidemics in a large community. For a community of uniformly mixing individuals an explicit expression is found for the critical vaccination coverage (CVC) and the effect of the vaccine response is determined entirely by the mean E(AB), where A and B, respectively, reflect the infectivity 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 adequate to describe the requirements for preventing epidemics when vaccination affects infectivity. The estimation of E(AB) poses a problem because A and B refer to the vaccine response of the same individual. Similar results are found when there are different types of individual, but now the mean E(AB) 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 vaccine response distribution. In practice this means that estimating a single measure of vaccine effectiveness is generally not enough to determine the CVC. For a specific community of households it is found that the vaccination coverage required to prevent epidemics decreases as the variation in the vaccine response increases.