# American Institute of Mathematical Sciences

2006, 3(3): 513-525. doi: 10.3934/mbe.2006.3.513

## Global dynamics of a staged progression model for infectious diseases

 1 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada 2 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Received  May 2005 Revised  January 2006 Published  May 2006

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.
Citation: Hongbin Guo, Michael Yi Li. Global dynamics of a staged progression model for infectious diseases. Mathematical Biosciences & Engineering, 2006, 3 (3) : 513-525. doi: 10.3934/mbe.2006.3.513
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