American Institute of Mathematical Sciences

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

Global dynamics of a staged progression model for infectious diseases

Hongbin Guo 1, and  Michael Yi Li 2,

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.
Keywords: staged progression, HIV/AIDS, mathematical model, global dynamics..
Mathematics Subject Classification: 92D3.
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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