Analytical threshold and stability results on age-structured epidemic models with vaccination

Abstract

This paper examines mathematical models for common childhood diseases such as measles and rubella and in particular the use of such models to predict whether or not an epidemic pattern of regular recurrent disease incidence will occur. We use age-structured compartmental models which divide the population amongst whom the disease is spreading into classes and use partial differential equations to model the spread of the disease. This paper is particularly concerned with an analytical investigation of the effects of different types of vaccination schemes. We examine possible equilibria and determine the stability of small oscillations about these equilibria. The results are important in predicting the long-term overall level of incidence of disease, in designing immunisation programs and in describing the variations of the incidence of disease about this equilibrium level.