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Mathematical Biosciences and Engineering

2020, Volume 17, Issue 3: 2569-2591. doi: 10.3934/mbe.2020141
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Viral infection dynamics in a spatial heterogeneous environment with cell-free and cell-to-cell transmissions

  • 1.
    Department of Mathematics, Tongji University, Shanghai 200092, China
  • 2.
    School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
  • Received: 29 December 2019 Accepted: 19 February 2020 Published: 02 March 2020

  • In this paper, we investigate a diffusive viral infection model in a spatial heterogeneous environment with two types of infection mechanisms and distinct dispersal rates for the susceptible and infected target cells. After establishing well-posedness of the model system, we identify the basic reproduction number R0 and explore the properties of R0 when the dispersal rate for infected target cells varies from zero to infinity. Moreover, we demonstrate that the basic reproduction number is a threshold parameter: the infection and virus will be cleared out if R0 ≤ 1, while if R0 > 1, the infection will persist and the model system admits at least one positive (chronic infection) steady state. For the special case when all model parameters are spatial homogeneous, this chronic infection steady state is unique and globally asymptotically stable.

    Citation: Zongwei Ma, Hongying Shu. Viral infection dynamics in a spatial heterogeneous environment with cell-free and cell-to-cell transmissions[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2569-2591. doi: 10.3934/mbe.2020141

    Related Papers:

  • In this paper, we investigate a diffusive viral infection model in a spatial heterogeneous environment with two types of infection mechanisms and distinct dispersal rates for the susceptible and infected target cells. After establishing well-posedness of the model system, we identify the basic reproduction number R0 and explore the properties of R0 when the dispersal rate for infected target cells varies from zero to infinity. Moreover, we demonstrate that the basic reproduction number is a threshold parameter: the infection and virus will be cleared out if R0 ≤ 1, while if R0 > 1, the infection will persist and the model system admits at least one positive (chronic infection) steady state. For the special case when all model parameters are spatial homogeneous, this chronic infection steady state is unique and globally asymptotically stable.


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