Guo, Hongbin; Li, Michael Y. Global dynamics of a staged progression model for infectious diseases. (English) Zbl 1092.92040 Math. Biosci. Eng. 3, No. 3, 513-525 (2006). Summary: 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 \(R_0\leq1\), 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. Cited in 57 Documents MSC: 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations Keywords:staged progression; HIV/AIDS; mathematical model; global dynamics PDFBibTeX XMLCite \textit{H. Guo} and \textit{M. Y. Li}, Math. Biosci. Eng. 3, No. 3, 513--525 (2006; Zbl 1092.92040) Full Text: DOI