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High-Throughput 2018, 7(4), 35; https://doi.org/10.3390/ht7040035

Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids

Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, 20650 Mohammedia, Morocco
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Received: 26 September 2018 / Revised: 8 November 2018 / Accepted: 13 November 2018 / Published: 19 November 2018
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Abstract

We model the transmission of the hepatitis B virus (HBV) by six differential equations that represent the reactions between HBV with DNA-containing capsids, the hepatocytes, the antibodies and the cytotoxic T-lymphocyte (CTL) cells. The intracellular delay and treatment are integrated into the model. The existence of the optimal control pair is supported and the characterization of this pair is given by the Pontryagin’s minimum principle. Note that one of them describes the effectiveness of medical treatment in restraining viral production, while the second stands for the success of drug treatment in blocking new infections. Using the finite difference approximation, the optimality system is derived and solved numerically. Finally, the numerical simulations are illustrated in order to determine the role of optimal treatment in preventing viral replication. View Full-Text
Keywords: HBV virus; abaptive immune response; treatment; numerical simulation HBV virus; abaptive immune response; treatment; numerical simulation
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Danane, J.; Allali, K. Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids. High-Throughput 2018, 7, 35.

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