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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Wissenschaftlicher Beirat: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

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1572-9176
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Stability analysis of delay integro-differential equations of HIV-1 infection model

Nigar Ali / Gul Zaman
  • Korrespondenzautor
  • Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan
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/ Il Hyo Jung
Online erschienen: 11.03.2018 | DOI: https://doi.org/10.1515/gmj-2018-0011

Abstract

In this paper, the analysis of an HIV-1 epidemic model is presented by incorporating a distributed intracellular delay. The delay term represents the latent period between the time that the target cells are contacted by the virus and the time the virions penetrated into the cells. To understand the analysis of our proposed model, the Rouths–Hurwiz criterion and general theory of delay differential equations are used. It is shown that the infection free equilibrium and the chronic-infection equilibrium are locally as well as globally asymptotically stable, under some conditions on the basic reproductive number R0. Furthermore, the obtained results show that the value of R0 can be decreased by increasing the delay. Therefore, any drugs that can prolong the latent period will help to control the HIV-1 infection.

Keywords: HIV-1 epidemic model; basic reproductive number; stability analysis

MSC 2010: 92D25; 49J15; 93D20; 91G20

References

  • [1]

    N. Ali, G. Zaman and O. Algahtani, Stability analysis of HIV-1 model with multiple delays, Adv. Difference Equ. 2016 (2016), Paper No. 88. Web of ScienceGoogle Scholar

  • [2]

    N. Ali, G. Zaman and M. Ikhlaq Chohan, Dynamical behavior of HIV-1 epidemic model with time dependent delay, J. Math. Comput. Sci. 6 (2016), no. 3, 377–389. Google Scholar

  • [3]

    R. V. Culshaw, S. Ruan and G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay, J. Math. Biol. 46 (2003), no. 5, 425–444. CrossrefGoogle Scholar

  • [4]

    F. R. Gantmacher, The Theory of Matrices. Vol. 1, Chelsea Publishing, New York, 1959. Google Scholar

  • [5]

    R. E. R. González, S. Coutinho, R. M. Zorzenon dos Santos and P. H. de Figueirêdo, Dynamics of the HIV infection under antiretroviral therapy: A cellular automata approach, Phys. A 392 (2013), no. 19, 4701–4716. CrossrefGoogle Scholar

  • [6]

    A. V. M. Herz, S. Bonhoeffer, R. M. Anderson, R. M. May and M. A. Nowak, Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay, Proc. Natl. Acad. Sci. USA 93 (1996), no. 14, 7247–7251. CrossrefGoogle Scholar

  • [7]

    A. V. Ion, Study of the behaviour of proliferating cells in leukemia modelled by a system of delay differential equations, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 23 (2015), no. 3, 65–81. Google Scholar

  • [8]

    X. Jiang, P. Yu, Z. Yuan and X. Zou, Dynamics of an HIV-1 therapy model of fighting a virus with another virus, J. Biol. Dyn. 3 (2009), no. 4, 387–409. CrossrefGoogle Scholar

  • [9]

    Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Math. Sci. Eng. 191, Academic Press, Boston, 1993. Google Scholar

  • [10]

    J. P. LaSalle, The Stability of Dynamical Systems, CBMS-NSF Regional Conf. Ser. in Appl. Math. 25, Society for Industrial and Applied Mathematics, Philadelphia, 1976. Google Scholar

  • [11]

    A. A. Lashari and G. Zaman, Optimal control of a vector borne disease with horizontal transmission, Nonlinear Anal. Real World Appl. 13 (2012), no. 1, 203–212. Web of ScienceCrossrefGoogle Scholar

  • [12]

    E. B. S. Marinho, F. S. Bacelar and R. F. S. Andrade, A model of partial differential equations for HIV propagation in lymph nodes, Phys. A 391 (2012), no. 1–2, 132–141. CrossrefGoogle Scholar

  • [13]

    J. E. Mittler, B. Markowitz, D. D. Ho and A. S. Perelson, Improved estimates for HIV-1 clearance rate and intracellular delay, AIDS 13 (1999), no. 11, 1415–1417. CrossrefGoogle Scholar

  • [14]

    P. W. Nelson, J. D. Murray and A. S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci. 163 (2000), no. 2, 201–215. CrossrefGoogle Scholar

  • [15]

    G. Nolan, Harnessing viral devices as pharmaceuticals: Fighting HIV-1’s fire with fire, Cell 90 (1997), no. 5, 821–824. CrossrefGoogle Scholar

  • [16]

    T. Revilla and G. Garcia-Ramos, Fighting a virus with a virus: A dynamical model for HIV-1 therapy, Math. Biosci. 185 (2003), no. 2, 191–203. CrossrefGoogle Scholar

  • [17]

    Y. Tian, Y. Bai and P. Yu, Impact of delay on HIV-1 dynamics of fighting a virus with another virus, Math. Biosci. Eng. 11 (2014), no. 5, 1181–1198. Web of ScienceCrossrefGoogle Scholar

  • [18]

    E. K. Wagner and M. J. Hewlett, Basic Virology, Blackwell Science, Malden, 1999. Google Scholar

  • [19]

    R. Xu, Global stability of an HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl. 375 (2011), no. 1, 75–81. Web of ScienceCrossrefGoogle Scholar

  • [20]

    P. Yu and X. Zou, Bifurcation analysis on an HIV-1 Model with constant injection of recombinant, Int. J. Bifurcation Chaos 22 (2012), no. 3, Article ID 1250062. Web of ScienceGoogle Scholar

  • [21]

    G. Zaman, A. A. Lashari and M. I. Chohan, Dynamical features of dengue disease with saturating incidence rate, Int. J. Pure Appl. Math. 76 (2012), no. 3, 383–402. Google Scholar

Artikelinformationen

Erhalten: 21.05.2016

Revidiert: 15.08.2017

Angenommen: 13.09.2017

Online erschienen: 11.03.2018


Quellenangabe: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0011.

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