A model for an SI disease in an age - structured population

We formulate and analyze a model for an infectious disease which does not cause death but for which infectives remain infective for life. We derive the basic reproductive number $R_0$ and show that there is a unique globally asymptotically stable equilibrium, namely the disease - free equilibrium if $R_0 < 1$ and the endemic equilibrium if $R_0 > 1$. However, the relation between the basic reproductive number, the mean age at infection, and the mean life span depends on the distribution of life spans and may be quite different from that for exponentially distributed life spans or very short infective periods.