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Dynamics of a generalized viral infection model with adaptive immune response

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Abstract

A mathematical model for viral infection is formulated by five nonlinear differential equations to describe the interactions between virus, host cells, and the adaptive immune response represented by cytotoxic T lymphocytes (CTL) cells and the antibodies. The infection transmission process is modeled by a general incidence function which covers several forms existing in models that studied viral infections such as HIV and HBV infections. Based on the direct Lyapunov method, the global stability of the equilibria is investigated. Furthermore, under certain hypotheses on the incidence function it is proved that the dynamical behavior of the model is fully characterized by the reproduction numbers for viral infection \(R_{0}\), for CTL immune response \(R_{1}^{z}\), for antibody immune response \(R_{1}^{w}\), for CTL immune competition \(R_{2}^{z}\) and for antibody immune competition \(R_{3}^{w}\).

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Acknowledgments

The authors thank the editor and the anonymous referees for very helpful suggestions and comments which have improved the presentation and content of the paper.

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Authors and Affiliations

  1. Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Derb Ghalef, 20340 , Casablanca, Morocco

    Khalid Hattaf

  2. Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P. O. Box 7955, Sidi Othman, Casablanca, Morocco

    Khalid Hattaf, Mostafa Khabouze & Noura Yousfi

Authors
  1. Khalid Hattaf
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  2. Mostafa Khabouze
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  3. Noura Yousfi
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Correspondence to Khalid Hattaf.

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Hattaf, K., Khabouze, M. & Yousfi, N. Dynamics of a generalized viral infection model with adaptive immune response. Int. J. Dynam. Control 3, 253–261 (2015). https://doi.org/10.1007/s40435-014-0130-5

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  • DOI: https://doi.org/10.1007/s40435-014-0130-5

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