Global dynamics of a staged progression model for infectious diseases

Abstract

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 R0: If R(0) =/< 1; then the disease-free equilibrium P(0) is globally asymptotically stable and the disease always dies out. If R(0) > 1; P0 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.