K. Ramalakshmi , B. Sundara Vadivoo , Kottakkaran Sooppy Nisar , Suliman Alsaeed
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引用次数: 0
Abstract
This study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the -Hilfer operator, we analyze the epidemic’s behavior. The research proposes control strategies, such as treatment and vaccination, aimed at reducing both acute and chronic infections. To achieve optimal control, we employ Pontryagin’s Maximum Principle. Through simulations, we demonstrate the effectiveness of our approach using the Non-Standard Two-Step Lagrange Interpolation Method (NS2LIM), supported by numerical findings and graphical representations. Additionally, we identify two control variables to minimize the populations of acute and chronic infections while enhancing recovery rates.
本研究探讨了乙型肝炎病毒（HBV）动态的数学模型，重点是其各个感染阶段，包括急性期和慢性期，以及传播途径。通过利用数学建模和带有 Θ-Hilfer 算子的分数微积分技术，我们分析了流行病的行为。研究提出了治疗和疫苗接种等控制策略，旨在减少急性和慢性感染。为了实现最优控制，我们采用了庞特里亚金最大原则（Pontryagin's Maximum Principle）。通过模拟，我们利用非标准两步拉格朗日插值法（NS2LIM）证明了我们方法的有效性，并辅以数值结果和图形表示。此外，我们还确定了两个控制变量，以尽量减少急性和慢性感染人群，同时提高恢复率。
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