Global properties for SIR and SEIR age-structured models

Abstract

We consider global asymptotic properties for the \emph{SIR} and \emph{SEIR} age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a~unique endemic steady state and the infection-free steady state.