Calculation of R₀ for age-of-infection models

We consider age-of-infection epidemic models to describe multiple-stage epidemic models, including treatment. We derive an expression for the basic reproduction number R_o in terms of the distributions of periods of stay in the various compartments. We find that, in the model without treatment, R_o depends only on the mean periods in compartments, and not on the form of the distributions. In treatment models, R_o depends on the form of the distributions of stay in infective compartments from which members are removed for treatment, but the dependence for treatment compartments is only on the mean stay in the compartments. The results give a considerable simplification in the calculation of the basic reproduction number.