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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 4: 859-877. doi: 10.3934/mbe.2015.12.859
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Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function

  • 1.
    School of Science and Technology, Zhejiang International Studies University, Hangzhou 310012
  • 2.
    Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250
  • 3.
    Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240
  • Published: 01 April 2015

  • MSC : Primary: 35L60, 92C37; Secondary: 35B35, 34K20.

  • In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number $\mathcal{R}_{0}$ of the model is obtained. We investigate the global behavior of the model in terms of $\mathcal{R}_{0}$: if $\mathcal{R}_{0}\leq1$, then the infection-free equilibrium is globally asymptotically stable, whereas if $\mathcal{R}_{0}>1$, then the infection equilibrium is globally asymptotically stable. Finally, some special cases, which reduce to some known HIV infection models studied by other researchers, are considered.

    Citation: Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function[J]. Mathematical Biosciences and Engineering, 2015, 12(4): 859-877. doi: 10.3934/mbe.2015.12.859

    Related Papers:

  • In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number $\mathcal{R}_{0}$ of the model is obtained. We investigate the global behavior of the model in terms of $\mathcal{R}_{0}$: if $\mathcal{R}_{0}\leq1$, then the infection-free equilibrium is globally asymptotically stable, whereas if $\mathcal{R}_{0}>1$, then the infection equilibrium is globally asymptotically stable. Finally, some special cases, which reduce to some known HIV infection models studied by other researchers, are considered.


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    [1] PLoS Comput. Biol., 4 (2008), e1000103, 9pp.
    [2] Math. Biosci. Eng., 10 (2013), 1335-1349.
    [3] Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017.
    [4] Math. Biosci., 165 (2000), 27-39.
    [5] Theoret. Pop. Biol., 56 (1999), 65-75.
    [6] J. Theoret. Biol., 190 (1998), 201-214.
    [7] SIAM. J. Appl. Math., 73 (2013), 572-593.
    [8] SIAM J. Appl. Math., 63 (2003), 1313-1327.
    [9] Mathematical Surveys and Monographs Vol 25, American Mathematical Society, Providence, RI, 1988.
    [10] SIAM J. Math. Anal., 20 (1989), 388-395.
    [11] Appl. Math. Lett., 22 (2009), 1690-1693.
    [12] Appl. Math. Lett., 24 (2011), 1199-1203.
    [13] SIAM J. Appl. Math., 70 (2010), 2693-2708.
    [14] SIAM J. Appl. Math., 72 (2012), 25-38.
    [15] J. Theoret. Biol., 185 (1997), 389-400.
    [16] Bull. Math. Biol., 58 (1996), 367-390.
    [17] Bull. Math. Biol., 72 (2010), 1492-1505.
    [18] SIAM J. Appl. Math., 70 (2010), 2434-2448.
    [19] Electron. J. Differential Equations, 65 (2001), 1-35.
    [20] Appl. Anal., 89 (2010), 1109-1140.
    [21] SIAM J. Appl. Math., 73 (2013), 1058-1095.
    [22] Commun. Pure Appl. Anal., 3 (2004), 695-727.
    [23] Math. Biosci. Eng., 9 (2012), 819-841.
    [24] Math. Biosci. Eng., 1 (2004), 267-288.
    [25] Science, 272 (1996), 74-79.
    [26] Oxford University Press, Oxford, 2000.
    [27] SIAM Rev., 41 (1999), 3-44.
    [28] SIAM. J. Appl. Math., 67 (2007), 731-756.
    [29] Differential Integral Equations, 3 (1990), 1035-1066.
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  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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