Global analysis of an infection age model with a class of nonlinear incidence rates

SIR infection age models with a very general class of nonlinear incidence rates f(S,J) are investigated. We give a necessary and sufficient condition for global asymptotic stability of the free-equilibrium related to the basic reproduction number. Furthermore, additional conditions allow us to prove an exponential stability of this disease-free equilibrium. Finally, by using a Lyapunov functional, we show the global asymptotic stability of the endemic equilibrium whenever it exists.