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Mathematical Biosciences and Engineering

2017, Volume 14, Issue 3: 805-820. doi: 10.3934/mbe.2017044
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A note on the global properties of an age-structured viral dynamic model with multiple target cell populations

  • 1.
    School of Mathematics and Statistics, Henan University, Kaifeng 475001, Henan, China
  • 2.
    Centre for Disease Modelling, York University, Toronto, Ontario, M3J 1P3, Canada
  • 3.
    Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
  • Received: 25 January 2016 Accepted: 30 October 2016 Published: 01 June 2017

  • MSC : Primary: 37B25, 92D25; Secondary: 35A24, 35M30

  • Some viruses can infect different classes of cells. The age of infection can affect the dynamics of infected cells and viral production. Here we develop a viral dynamic model with the age of infection and multiple target cell populations. Using the methods of semigroup and Lyapunov function, we study the global asymptotic property of the steady states of the model. The results show that when the basic reproductive number falls below 1, the infection is predicted to die out. When the basic reproductive number exceeds 1, there exists a unique infected steady state which is globally asymptotically stable. The model can be extended to study virus dynamics with multiple compartments or coinfection by multiple types of viruses. We also show that under some scenarios the age-structured model can be reduced to an ordinary differential equation system with or without time delays.

    Citation: Shaoli Wang, Jianhong Wu, Libin Rong. A note on the global properties of an age-structured viral dynamic model with multiple target cell populations[J]. Mathematical Biosciences and Engineering, 2017, 14(3): 805-820. doi: 10.3934/mbe.2017044

    Related Papers:

  • Some viruses can infect different classes of cells. The age of infection can affect the dynamics of infected cells and viral production. Here we develop a viral dynamic model with the age of infection and multiple target cell populations. Using the methods of semigroup and Lyapunov function, we study the global asymptotic property of the steady states of the model. The results show that when the basic reproductive number falls below 1, the infection is predicted to die out. When the basic reproductive number exceeds 1, there exists a unique infected steady state which is globally asymptotically stable. The model can be extended to study virus dynamics with multiple compartments or coinfection by multiple types of viruses. We also show that under some scenarios the age-structured model can be reduced to an ordinary differential equation system with or without time delays.


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