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Stability analysis of humoral immunity HIV infection models with RTI and discrete delays

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Abstract

A class of HIV infection models are proposed and analyzed. The models incorporate three types of immune cells, CD4\(^{+}\) T cells, macrophages and B cells. We consider also two types of intracellular discrete delays to describe the latent period from the virus contacts an uninfected target cell and the production of new HIV particles. The infection rate is represented by bilinear incidence and saturation incidence in the first two models. In the third model, both the infection rate and neutralization rate of viruses are given by nonlinear general functions. Two bifurcation parameters, the basic reproduction number and the humoral immunity activation number are derived. We established a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. We utilize Lyapunov method to investigate the global asymptotic stability of all steady states of the models. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt

    A. M. Shehata & A. M. Elaiw

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    A. M. Elaiw

  3. Department of Mathematics, Faculty of Science, Sohag University, Sohâg, Egypt

    E. Kh. Elnahary & M. Abul-Ez

Authors
  1. A. M. Shehata
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  2. A. M. Elaiw
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  3. E. Kh. Elnahary
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  4. M. Abul-Ez
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Correspondence to A. M. Elaiw.

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Shehata, A.M., Elaiw, A.M., Elnahary, E.K. et al. Stability analysis of humoral immunity HIV infection models with RTI and discrete delays. Int. J. Dynam. Control 5, 811–831 (2017). https://doi.org/10.1007/s40435-016-0235-0

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  • DOI: https://doi.org/10.1007/s40435-016-0235-0

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