Semiparametric estimation of the duration of immunity from infectious disease time series: influenza as a case-study

An important epidemiological problem is to estimate the decay through time of immunity following infection. For this purpose, we propose a semiparametric time series epidemic model that is based on the mechanism of the susceptible-infected-recovered-susceptible system to analyse complex time series data. We develop an estimation method for the model. Simulations show that the approach proposed can capture the non-linearity of epidemics as well as estimate the decay of immunity. We apply our approach to influenza in France and the Netherlands and show a rapid decline in immunity following infection, which agrees with recent spatiotemporal analyses. Copyright 2005 Royal Statistical Society.