Calculation of $R_0$ for age-of-infection models - Christine K. Yang; Fred Brauer (Mathematical Biosciences and Engineering)
We consider age-of-infection epidemic models to describe multiple-stage epidemic models, including treatment. We derive an expression for thebasic reproduction number $R_0$ in terms of the distributions of periods of stayin the various compartments. We find that, in the model without treatment,$R_0$ depends only on the mean periods in compartments, and not on the formof the distributions. In treatment models, $R_0$ depends on the form of the dis-tributions of stay in infective compartments from which members are removedfor treatment, but the dependence for treatment compartments is only on themean stay in the compartments. The results give a considerable simplificationin the calculation of the basic reproduction number.