Global dynamics of a discrete age-structured SIR epidemic model with applications to measles vaccination strategies

•New results on the global stability of the endemic equilibrium of a class of epidemic models with a discrete age-structure.•Adapted the model to study vaccination strategies of measles.•We calibrated an age-group model for measles vaccination using published data on measles incidence from India, and compared the effects of two different measles vaccination strategies proposed by the Ministry of Health of India. We investigate an SIR epidemic model with discrete age groups to understand the transmission dynamics of an infectious disease in a host population with an age structure. We derive the basic reproduction number R0 and show that it is a sharp threshold parameter. If R0≤1, the disease-free equilibrium E0 is globally stable. If R0>1,E0 is unstable, the model is uniformly persistent, and an endemic equilibrium exists. The global stability of the endemic equilibrium when R0>1 is established under a sufficient condition. The model is then used to analyze the measles data in India and evaluate the effectiveness of several vaccination strategies for the control of measles epidemics in India.