冠状病毒病分数阶SIQ数学模型的非标准有限差分格式数值模拟

IF 0.5 Q3 MATHEMATICS
N. Raza, A. Bakar, A. Khan, C. Tunç
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引用次数: 3

摘要

针对冠状病毒病,提出了一种新的带有Caputo导数的非线性分数阶大流行模型。提出了一种非标准有限差分(NSFD)方法对该模型进行数值求解。这种策略保留了解的一些最重要的物理性质,如非负性、有界性和稳定性或收敛到稳定的稳态。分析了模型的平衡点,确定了分数阶模型在平衡点处是局部渐近稳定的。证明了该模型解的非负性和有界性。利用不动点理论证明了解的存在唯一性。计算基本繁殖数以研究冠状病毒病的动态。值得一提的是,非整数导数使我们对日冕模型的动态复杂性有了更深入的了解。建议的技术产生动态一致的结果,并与分析工作非常匹配。为了说明我们的结果,我们在不同的检疫水平上对提出的模型进行了全面的定量研究。数值模拟表明,如果人们在保持足够的知识的同时,在不同的覆盖范围内实施强制性隔离措施,就可以迅速根除大流行。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical Simulations of the Fractional-Order SIQ Mathematical Model of Corona Virus Disease Using the Nonstandard Finite Difference Scheme
This paper proposes a novel nonlinear fractional-order pandemic model with Caputo derivative for corona virus disease. A nonstandard finite difference (NSFD) approach is presented to solve this model numerically. This strategy preserves some of the most significant physical properties of the solution such as non-negativity, boundedness and stability or convergence to a stable steady state. The equilibrium points of the model are analyzed and it is determined that the proposed fractional model is locally asymptotically stable at these points. Non-negativity and boundedness of the solution are proved for the considered model. Fixed point theory is employed for the existence and uniqueness of the solution. The basic reproduction number is computed to investigate the dynamics of corona virus disease. It is worth mentioning that the non-integer derivative gives significantly more insight into the dynamic complexity of the corona model. The suggested technique produces dynamically consistent outcomes and excellently matches the analytical works. To illustrate our results, we conduct a comprehensive quantitative study of the proposed model at various quarantine levels. Numerical simulations show that can eradicate a pandemic quickly if a human population implements obligatory quarantine measures at varying coverage levels while maintaining sufficient knowledge.
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来源期刊
CiteScore
1.10
自引率
20.00%
发文量
0
期刊介绍: The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.
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