Mathematical Analysis of the Transmission Dynamics of Hepatitis B Virus

IF 1.5 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Festus Abiodun Oguntolu, Olumuyiwa James Peter, Dipo Aldila, Ghaniyyat Bolanle Balogun, Oyinlola Patricia Ogunmola, Benjamin Idoko Omede
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Abstract

Hepatitis B is a life-threatening hepatic illness induced by the Hepatitis B virus (HBV). This is a major worldwide health issue, especially in low- and middle-income nations in Africa and the Western Pacific, where prevalence rates are the greatest. Nevertheless, the existence of an efficacious vaccination, Hepatitis B persists in inflicting significant morbidity and death owing to a deficiency of awareness regarding the illness. Thus, we developed a deterministic mathematical model to elucidate the transmission dynamics of Hepatitis B, integrating elements such as vertical transmission, re-infection, and environmental viral concentration. The study starts with the calculation of the basic reproduction number and the assessment of the local stability of the disease-free equilibrium employing the Routh-Hurwitz criteria. A comprehensive examination of the model indicates that the model may experience backward bifurcation phenomena under some specific conditions. This trait presents considerable challenges in the proper management of Hepatitis B infection among the population. Assuming no re-infection of Hepatitis B post-recovery, the disease-free equilibrium point is globally asymptotically stable when the basic reproduction number is less than or equal to one. The sensitivity analysis of the basic reproduction number was conducted to assess the influence of each fundamental parameter in the model that contributes to disease transmission. Utilizing the optimal control theory to effectively curb the spread of Hepatitis B, we incorporated two time-varying control strategies, namely the prevention of susceptible individuals from acquiring HBV (through safe sex practice, regular washing of hands, and using protective hand gloves when handling blood, body fluid and semen) and the sensitization on individuals on personal hygiene, sterilization and proper disposal of medical and dental equipment like syringes in order to reduce the shedding of HBV in the environment. The numerical simulations indicated that Hepatitis B infection may be effectively managed and mitigated within the community if both control measures are correctly implemented.

乙型肝炎病毒传播动力学的数学分析
乙型肝炎是由乙型肝炎病毒(HBV)引起的一种危及生命的肝脏疾病。这是一个重大的世界卫生问题,特别是在患病率最高的非洲和西太平洋的低收入和中等收入国家。然而,尽管存在有效的疫苗接种,由于缺乏对这种疾病的认识,乙型肝炎仍然造成大量发病率和死亡。因此,我们开发了一个确定性数学模型来阐明乙型肝炎的传播动力学,整合了垂直传播、再感染和环境病毒浓度等因素。本研究从计算基本繁殖数和利用劳斯-赫维茨准则评估无病平衡的局部稳定性开始。对该模型的综合考察表明,在某些特定条件下,该模型可能出现后向分岔现象。这一特点对人群中乙型肝炎感染的适当管理提出了相当大的挑战。假设康复后无乙肝再感染,当基本繁殖数小于等于1时,无病平衡点全局渐近稳定。对基本繁殖数进行敏感性分析,评估模型中各基本参数对疾病传播的影响。利用最优控制理论有效遏制乙型肝炎的传播,我们结合了两种时变控制策略,即预防易感个体感染HBV(通过安全性行为、经常洗手、在处理血液、体液和精液时使用防护手套)和个人卫生敏感化。消毒和妥善处置注射器等医疗和牙科设备,以减少乙肝病毒在环境中的传播。数值模拟结果显示,如果正确实施这两项控制措施,可以有效地管理和减轻社区内的乙型肝炎感染。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Brazilian Journal of Physics
Brazilian Journal of Physics 物理-物理:综合
CiteScore
2.50
自引率
6.20%
发文量
189
审稿时长
6.0 months
期刊介绍: The Brazilian Journal of Physics is a peer-reviewed international journal published by the Brazilian Physical Society (SBF). The journal publishes new and original research results from all areas of physics, obtained in Brazil and from anywhere else in the world. Contents include theoretical, practical and experimental papers as well as high-quality review papers. Submissions should follow the generally accepted structure for journal articles with basic elements: title, abstract, introduction, results, conclusions, and references.
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