Sweilam Nasser, Al-Mekhlafi Seham, Shatta Salma, Baleanu Dumitru
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.
Department of Mathematics, Faculty of Education, Sana'a University, Yemen.
Results Phys. 2022 Nov;42:105964. doi: 10.1016/j.rinp.2022.105964. Epub 2022 Sep 5.
In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.
本文提出了一种具有修正参数的新型变阶新冠病毒疾病（COVID - 19）模型。变阶分数阶导数是在卡普托（Caputo）意义下定义的。这里给出了两种变阶卡普托定义。推导了该模型的基本再生数。对所提出模型的性质进行了理论分析和数值研究。使用两种数值方法对所建议的最优控制模型进行了研究。这两种方法分别是非标准广义四阶龙格 - 库塔方法和非标准广义五阶龙格 - 库塔技术。此外，还研究了所提方法的稳定性。为了证明这些方法的简单性和有效性，给出了数值测试示例以及与埃及和意大利实际数据的比较。
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