A School-Oriented, Age-Structured Epidemic Model

Abstract

A model of childhood epidemics focusing on the impact of the school-year is presented. At the onset of the epidemic season, a new cohort of susceptible students enter the school, all other age-classes advance one year, while the oldest age-group leaves the mixing pool. If the susceptible pool is sufficiently large at the onset of the season, an epidemic will arise and run to its conclusion prior to the end of the school-year. The system is expressed in terms of a discrete dynamical system giving the changes in the age-dependent immunity structure on a year-to-year basis. If disease transmission is independent of age, the system settles at epidemics of constant size in each season. If disease transmission is age-dependent, more complicated dynamics may occur, including multiple stable states and chaos.