Using age of infection models to derive an explicit expression for R 0 by Christine

Using a multiple stage age of infection model, we derive an expression for the basic reproduction number, R0. We apply this method to find R0 in analogous treatment models. We find, in the model without treatment, R0 depends only on the mean infective period, and not on the infective distribution. In treatment models, R0 depends on the mean infective and mean treatment period, as well as the distribution of the infective period, but not on the distribution of the treatment period. With an explicit formula for R0 and the final size relation, we provide a practical alternative to evaluating the effect of treatment and other control measures. We compare our models to previous models of SARS and TB.