{"title":"Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids.","authors":"Jaouad Danane, Karam Allali","doi":"10.3390/ht7040035","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":53433,"journal":{"name":"High-Throughput","volume":"7 4","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6306857/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"High-Throughput","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/ht7040035","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Biochemistry, Genetics and Molecular Biology","Score":null,"Total":0}
引用次数: 0
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.
我们用六个微分方程来模拟乙型肝炎病毒（HBV）的传播，这六个微分方程代表了 HBV 与含 DNA 的囊壳、肝细胞、抗体和细胞毒性 T 淋巴细胞（CTL）之间的反应。细胞内延迟和治疗被整合到模型中。模型支持最优控制对的存在，庞特里亚金最小原理给出了最优控制对的特征。需要注意的是，其中一个控制对描述了药物治疗在抑制病毒产生方面的有效性，而第二个控制对则代表了药物治疗在阻止新感染方面的成功率。利用有限差分近似法，可以推导出最优化系统并进行数值求解。最后，对数值模拟进行说明，以确定最佳治疗在防止病毒复制方面的作用。
High-ThroughputBiochemistry, Genetics and Molecular Biology-Biotechnology
CiteScore
3.60
自引率
0.00%
发文量
0
审稿时长
9 weeks
期刊介绍：
High-Throughput (formerly Microarrays, ISSN 2076-3905) is a multidisciplinary peer-reviewed scientific journal that provides an advanced forum for the publication of studies reporting high-dimensional approaches and developments in Life Sciences, Chemistry and related fields. Our aim is to encourage scientists to publish their experimental and theoretical results based on high-throughput techniques as well as computational and statistical tools for data analysis and interpretation. The full experimental or methodological details must be provided so that the results can be reproduced. There is no restriction on the length of the papers. High-Throughput invites submissions covering several topics, including, but not limited to: -Microarrays -DNA Sequencing -RNA Sequencing -Protein Identification and Quantification -Cell-based Approaches -Omics Technologies -Imaging -Bioinformatics -Computational Biology/Chemistry -Statistics -Integrative Omics -Drug Discovery and Development -Microfluidics -Lab-on-a-chip -Data Mining -Databases -Multiplex Assays
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