A class of SIR epidemic model with saturation incidence and age of infection

Saturating contact rate of individual contacts is very important in an epidemiology model. A class of SIR model with saturation incidence and age of infection is formulated in this paper. The dynamical behavior of the model is studied and the basic reproductive number R₀ is defined. It is proved that the diseased-free equilibrium is globally asymptotically stable if R₀ < 1. The endemic equilibrium is locally asymptotically stable if K₁ > alpha and R₀ > 1.