Khan Amir, Zarin Rahat, Khan Saddam, Saeed Anwar, Gul Taza, Humphries Usa Wannasingha
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), Bangkok, Thailand.
Department of Mathematics and Statistics, University of Swat, Swat, Pakistan.
Comput Methods Biomech Biomed Engin. 2022 May;25(6):619-640. doi: 10.1080/10255842.2021.1972096. Epub 2021 Nov 1.
In this research, COVID-19 model is formulated by incorporating harmonic mean type incidence rate which is more realistic in average speed. Basic reproduction number, equilibrium points, and stability of the proposed model is established under certain conditions. Runge-Kutta fourth order approximation is used to solve the deterministic model. The model is then fractionalized by using Caputo-Fabrizio derivative and the existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Adam-Moulton scheme. Sensitivity analysis of the proposed deterministic model is studied to identify those parameters which are highly influential on basic reproduction number.
在本研究中，通过纳入在平均速度方面更符合实际的调和平均型发病率来构建COVID-19模型。在一定条件下建立了所提模型的基本再生数、平衡点和稳定性。采用四阶龙格-库塔近似法求解确定性模型。然后利用卡普托-法布里齐奥导数对模型进行分数阶化，并通过巴拿赫定理和勒雷-绍德尔择一定理证明了解的存在性和唯一性。对于分数阶数值模拟，我们使用亚当-莫尔顿格式。对所提确定性模型进行敏感性分析，以确定那些对基本再生数有高度影响的参数。
