The basic reproduction number of an infectious disease in a stable population: The impact of population growth rate on the eradication threshold

Abstract

Although age-related heterogeneity of infection has been addressed in various epidemic models assuming a demographically stationary population, only a few studies have explicitly 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 to account for the non-stationality of the host population. The basic reproduction number R 0 is derived using the next generation operator, permitting discussions over the well-known invasion principles. The condition of endemic steady state is also characterized by using the effective next generation operator. Subsequently, estimators of R 0 are offered which can explicitly account for non-zero population growth rate. Critical coverages of vaccination are also shown, highlighting the threshold condition for a population with varying size. When quantifying R 0 using the force of infection estimated from serological data, it should be remembered that the estimate increases as the population growth rate decreases. On the contrary, given the same R 0, critical coverage of vaccination in a growing population would be higher than that of decreasing population. Our exercise implies that high mass vaccination coverage at an early age would be needed to control childhood vaccine-preventable diseases in developing countries.