Global dynamics of a staged progression model for infectious diseases

We analyze a mathematical model for infectious diseases that progress through distinct stages within infected hosts. An example of such a disease is AIDS, which results from HIV infection. For a general $n$-stage stage-progression (SP) model with bilinear incidences, we prove that the global dynamics are completely determined by the basic reproduction number $R_0.$ If $R_0\le 1,$ then the disease-free equilibrium $P_0$ is globally asymptotically stable and the disease always dies out. If $R_0>1,$ $P_0$ is unstable, and a unique endemic equilibrium $P^*$ is globally asymptotically stable, and the disease persists at the endemic equilibrium. The basic reproduction numbers for the SP model with density dependent incidence forms are also discussed.