Effects of vaccination programmes on transmission rates of infections and related threshold conditions for control

This study addresses the problem of the existence of conditions for persistence or eradication of age-dependent directly transmitted infections. The usual system of differential equations describing the dynamics of the disease is transformed into integral equations. The authors show how to solve these equations and, by applying the contraction mapping theorem, give conditions for the persistence or eradication of the infection. A practical illustration of the application of the methods proposed is sketched, using data for rubella collected from a small Brazilian community.