The Basic Reproduction Number of an Infectious Diseasein a Stable Population:The Impact of Population Growth Rateon the Eradication Threshold

Abstract

Although age-related heterogeneity of infection has been addressed in variousepidemic models assuming a demographically stationary population, only a few studies haveexplicitly dealt with age-specific patterns of transmission in growing or decreasing population.To discuss the threshold principle realistically, the present study investigates an age-duration-structured SIR epidemic model assuming a stable host population, as the first scheme toaccount for the non-stationality of the host population. The basic reproduction number R₀is derived using the next generation operator, permitting discussions over the well-knowninvasion principles. The condition of endemic steady state is also characterized by usingthe effective next generation operator. Subsequently, estimators of R₀ are offered which canexplicitly account for non-zero population growth rate. Critical coverages of vaccination arealso shown, highlighting the threshold condition for a population with varying size. Whenquantifying R₀ using the force of infection estimated from serological data, it should beremembered that the estimate increases as the population growth rate decreases. On thecontrary, given the same R₀, critical coverage of vaccination in a growing population would behigher than that of decreasing population. Our exercise implies that high mass vaccinationcoverage at an early age would be needed to control childhood vaccine-preventable diseasesin developing countries.