The relation between the force of infection and the observed age distribution of immunity, or cases, is formalized in the so-called catalytic model, which equates the estimation of the force of infection to classic hazard regression Griffiths 1974Grenfell 1985.  In this formulation, the classic estimator for R0 based on the mean age of infection (above) is a special case for the setting in which the force of infection is constant over an individuals lifetime and the population dynamics (birth and death rates) are constant.  This method has been invaluable for the analysis of infections, like rubella, for which long-term time series are rarely available, but cross-sectional case reports are.  Lessler and Metcalf Lessler 2013 used this method to estimate R0 for rubella for 40 African countries and illustrated significant county-to-country variation in the R0 of rubella ranging from 3-8.