Global dynamics of a staged progression model for infectious diseases

  • 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 $R_0.$ 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[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 $R_0.$ 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.


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