Kermack and McKendrick revisited: The variable susceptibility model for infectious diseases

In this paper, we reformulate Kermack's and McKendrick's variable susceptibility model for infectious diseases as a nonlinear age-dependent population dynamics model, then we prove an existence and uniqueness result for the endemic steady state. Subsequently we discuss the local stability of the endemic steady state. Finally we show that Pease's evolutionary epidemic model can be seen as a special case of the variable susceptibility model and discuss possible extensions.