用分数算子分析 COVID-19 流行病的干预影响

S. Bhatter, Sangeeta Kumawat, Bhamini Bhatia, S. Purohit
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引用次数: 0

摘要

本研究引入了一种创新的分数方法来分析 COVID-19 的爆发动态,研究封锁、隔离和隔离等干预策略对疾病传播的影响。该分析结合了卡普托分式导数,以把握感染进展过程中的长期记忆效应和非局部行为。重点是评估解的有界性和非负性。此外,我们还利用 Lipschitz 和 Banach 收缩定理来验证解的存在性和唯一性。我们利用下一代矩阵技术确定了与模型相关的基本繁殖数。随后,通过使用归一化敏感性指数,我们对基本繁殖数进行了敏感性分析,从而有效地确定了模型的控制参数。为了验证我们的理论发现,我们利用两步拉格朗日插值技术对各种分数阶值进行了数值模拟。此外,该模型的数值算法以图形表示,以说明所提方法的有效性,并分析任意阶导数对疾病动力学的影响。
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Analysis of COVID-19 epidemic with intervention impacts by a fractional operator
This study introduces an innovative fractional methodology for analyzing the dynamics of COVID-19 outbreak, examining the impact of intervention strategies like lockdown, quarantine, and isolation on disease transmission. The analysis incorporates the Caputo fractional derivative to grasp long-term memory effects and non-local behavior in the advancement of the infection. Emphasis is placed on assessing the boundedness and non-negativity of the solutions. Additionally, the Lipschitz and Banach contraction theorem are utilized to validate the existence and uniqueness of the solution. We determine the basic reproduction number associated with the model utilizing the next generation matrix technique. Subsequently, by employing the normalized sensitivity index, we perform a sensitivity analysis of the basic reproduction number to effectively identify the controlling parameters of the model. To validate our theoretical findings, numerical simulations are conducted for various fractional order values, utilizing a two-step Lagrange interpolation technique. Furthermore, the numerical algorithms of the model are represented graphically to illustrate the effectiveness of the proposed methodology and to analyze the effect of arbitrary order derivatives on disease dynamics.
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