Estimation of infectious disease parameters from serological survey data: the impact of regular epidemics

Serological surveys are a useful source of information about epidemiological parameters for infectious diseases. In particular they may be used to estimate contact rates, forces of infection, the reproduction number and the critical vaccination threshold. However, these estimation methods require the assumption that the infection is in endemic equilibrium. Such equilibria seldom exist in practice: for example, many common infections of childhood exhibit regular epidemic cycles. In this paper, we investigate whether ignoring such cycles produces biased estimates. We apply the methods to data on mumps and rubella in the U.K. prior to the introduction of the combined measles, mumps, rubella (MMR) vaccine. We conclude that past epidemics have only a marginal effect on estimates, and that standard methods that do not adjust for regular epidemics are valid.