Maximal prevalence and the basic reproduction number in simple epidemics

Abstract

For the basic versions of the SIR and SIRS epidemic models estimates for the maximal prevalence are computed in terms of the basic reproduction number and other relevant quantities. Maximal prevalence is studied as a function of the rate of loss of immunity. Total size and total cost (total infected time) of the epidemic are estimated. For SIR models with demographic renewal it is investigated whether prevalence is a monotone function of the renewal rate.