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Numerical Analysis for a Fractional Differential Time‐Delay Model of HIV Infection of CD4+ T‐Cell Proliferation under Antiretroviral Therapy

Author

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  • Yiliang Liu
  • Peifen Lu
  • Ivan Szanto

Abstract

We study a fractional differential model of HIV infection of CD4+ T‐cell, in which the CD4+ T‐cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for τ ≥ 0. We calculate the basic reproduction number R0, the IFE E0, two IPEs E1* and E2*, and so on, and judge the stability of the equilibrium. In addition, we describe the dynamic behaviors of the fractional HIV model by using the Adams‐type predictor‐corrector method algorithm. At last, we extend the model to incorporate the term which we consider the loss of virion and a bilinear term during attacking the target cells.

Suggested Citation

  • Yiliang Liu & Peifen Lu & Ivan Szanto, 2014. "Numerical Analysis for a Fractional Differential Time‐Delay Model of HIV Infection of CD4+ T‐Cell Proliferation under Antiretroviral Therapy," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:291614
    DOI: 10.1155/2014/291614
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    References listed on IDEAS

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    3. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
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