Wang Bo, Mondal Jayanta, Samui Piu, Chatterjee Amar Nath, Yusuf Abdullahi
School of Electronic Information and Automation, Aba Teachers University, Wenchuan, 623002 China.
School of Applied Mathematics, University Electronic Science and Technology of China, Chengdu, 610054 China.
Eur Phys J Spec Top. 2022;231(10):1915-1929. doi: 10.1140/epjs/s11734-022-00454-4. Epub 2022 Feb 1.
In December 2019, a novel coronavirus disease (COVID-19) appeared in Wuhan, China. After that, it spread rapidly all over the world. Novel coronavirus belongs to the family of Coronaviridae and this new strain is called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epithelial cells of our throat and lungs are the main target area of the SARS-CoV-2 virus which leads to COVID-19 disease. In this article, we propose a mathematical model for examining the effects of antiviral treatment over viral mutation to control disease transmission. We have considered here three populations namely uninfected epithelial cells, infected epithelial cells, and SARS-CoV-2 virus. To explore the model in light of the optimal control-theoretic strategy, we use Pontryagin's maximum principle. We also illustrate the existence of the optimal control and the effectiveness of the optimal control is studied here. Cost-effectiveness and efficiency analysis confirms that time-dependent antiviral controlled drug therapy can reduce the viral load and infection process at a low cost. Numerical simulations have been done to illustrate our analytical findings. In addition, a new variable-order fractional model is proposed to investigate the effect of antiviral treatment over viral mutation to control disease transmission. Considering the superiority of fractional order calculus in the modeling of systems and processes, the proposed variable-order fractional model can provide more accurate insight for the modeling of the disease. Then through the genetic algorithm, optimal treatment is presented, and its numerical simulations are illustrated.
2019年12月，一种新型冠状病毒疾病（COVID-19）在中国武汉出现。此后，它在全球迅速传播。新型冠状病毒属于冠状病毒科，这种新毒株被称为严重急性呼吸综合征冠状病毒2（SARS-CoV-2）。我们咽喉和肺部的上皮细胞是导致COVID-19疾病的SARS-CoV-2病毒的主要靶区。在本文中，我们提出了一个数学模型，用于研究抗病毒治疗对病毒突变的影响，以控制疾病传播。我们在此考虑了三个群体，即未感染的上皮细胞、感染的上皮细胞和SARS-CoV-2病毒。为了根据最优控制理论策略探索该模型，我们使用庞特里亚金极大值原理。我们还阐述了最优控制的存在性，并在此研究了最优控制的有效性。成本效益和效率分析证实，时间依赖的抗病毒控制药物疗法可以以低成本降低病毒载量和感染过程。已进行数值模拟以说明我们的分析结果。此外，还提出了一个新的变阶分数模型，以研究抗病毒治疗对病毒突变的影响，以控制疾病传播。考虑到分数阶微积分在系统和过程建模中的优越性，所提出的变阶分数模型可以为该疾病的建模提供更准确的见解。然后通过遗传算法，给出了最优治疗方案，并对其进行了数值模拟说明。
