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Mathematical Biosciences and Engineering

2006, Volume 3, Issue 3: 513-525. doi: 10.3934/mbe.2006.3.513
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Global dynamics of a staged progression model for infectious diseases

  • 1.
    Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1
  • 2.
    Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1
  • Received: 01 May 2005 Accepted: 29 June 2018 Published: 01 May 2006

  • MSC : 92D30.

  • 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 R0≤1, then the disease-free equilibrium P0 is globally asymptotically stable and the disease always dies out. If R0>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.

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

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  • 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 R0≤1, then the disease-free equilibrium P0 is globally asymptotically stable and the disease always dies out. If R0>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.


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