Stability of the endemic equilibrium in epidemic models with subpopulations

For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.