Analytical Results on the Stability of Age-Structured Recurrent Epidemic Models

Abstract

This paper examines the equilibrium and stability properties of relatively simple mathematical models for the transmission of infectious diseases such as measles, rubella, and mumps. We consider endemic diseases which are recurrent over a long time period. We discuss some simple models which incorporate an age structure into the population amongst whom the disease is spreading, since recent work has shown this feature to be important. The results are relevant in three ways: for predicting the long-term overall level of incidence of disease; for describing the oscillations of the incidence of disease around this equilibrium level; and for designing immunization programmes.