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Optimal control of a delayed hepatitis B viral infection model with cytotoxic T-lymphocyte and antibody responses

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Abstract

The dynamics of a model describing the hepatitis B viral infection model with cytotoxic T-lymphocyte and antibody responses is studied in this paper. The model consists of a system of differential equations describing the interaction between hepatocytes, the free virus and the immune responses. Both the treatment and the intracellular delay are incorporated into the model. Existence, positivity and boundedness of solutions are investigated. Also, the existence of the optimal control pair is established and the Pontryagin’s minimum principle is used to characterize these optimal controls. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. The optimality system is derived and solved numerically using the forward and backward difference approximation. The obtained results show that the optimal treatment strategies reduce the viral load and then increase the uninfected hepatocytes, this improves the patient life quality.

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Acknowledgments

The authors are grateful to the editor-in-chief and the anonymous reviewers for their helpful comments and suggestions during the revisions process which improved the manuscript considerably.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Techniques, Mohammedia, University Hassan II-Casablanca, PO Box 146, Mohammedia, Morocco

    Adil Meskaf & Karam Allali

  2. Department of SEG, Faculty Polydisciplinary of El Jadida, University Chouaib Doukkali, El Jadida, Morocco

    Youssef Tabit

Authors
  1. Adil Meskaf
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  2. Karam Allali
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  3. Youssef Tabit
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Correspondence to Karam Allali.

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Meskaf, A., Allali, K. & Tabit, Y. Optimal control of a delayed hepatitis B viral infection model with cytotoxic T-lymphocyte and antibody responses. Int. J. Dynam. Control 5, 893–902 (2017). https://doi.org/10.1007/s40435-016-0231-4

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  • DOI: https://doi.org/10.1007/s40435-016-0231-4

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