Exploring the relationship between incidence and the average age of infection during seasonal epidemics

Abstract

The inverse relationship between the incidence and the average age of first infection for immunizing agents has become a basic tenet in the theory underlying the mathematical modeling of infectious diseases. However, this relationship assumes that the infection has reached an endemic equilibrium. In reality, most infectious diseases exhibit seasonal and/or long-term oscillations in incidence. We use a seasonally forced age-structured SIR model to explore the relationship between the number of cases and the average age of first infection over a single epidemic cycle. Contrary to the relationship for the equilibrium dynamics, we find that the average age of first infection is greatest at or near the peak of the epidemic when mixing is homogeneous. We explore the sensitivity of our findings to assumptions about the natural history of infection, population mixing behavior, the mechanism of seasonality, and of the timing of case reporting in relation to the infectious period. We conclude that seasonal variation in the average age of first infection tends to be greatest for acute infections, and the relationship between the number of cases and the average age of first infection can vary depending on the nature of population mixing and the natural history of infection.