Abdo Mohammed S, Shah Kamal, Wahash Hanan A, Panchal Satish K
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S), 431001, India.
Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen.
Chaos Solitons Fractals. 2020 Jun;135:109867. doi: 10.1016/j.chaos.2020.109867. Epub 2020 May 8.
The major purpose of the presented study is to analyze and find the solution for the model of nonlinear fractional differential equations (FDEs) describing the deadly and most parlous virus so-called coronavirus (COVID-19). The mathematical model depending of fourteen nonlinear FDEs is presented and the corresponding numerical results are studied by applying the fractional Adams Bashforth (AB) method. Moreover, a recently introduced fractional nonlocal operator known as Atangana-Baleanu (AB) is applied in order to realize more effectively. For the current results, the fixed point theorems of Krasnoselskii and Banach are hired to present the existence, uniqueness as well as stability of the model. For numerical simulations, the behavior of the approximate solution is presented in terms of graphs through various fractional orders. Finally, a brief discussion on conclusion about the simulation is given to describe how the transmission dynamics of infection take place in society.
本研究的主要目的是分析并找到描述致命且最危险的病毒——冠状病毒（COVID-19）的非线性分数阶微分方程（FDEs）模型的解决方案。提出了一个由14个非线性FDEs组成的数学模型，并应用分数阶亚当斯-巴什福思（AB）方法研究了相应的数值结果。此外，为了更有效地实现，应用了最近引入的一种称为阿坦加纳-巴莱亚努（AB）的分数阶非局部算子。对于当前结果，利用克拉索夫斯基和巴拿赫的不动点定理来阐述模型的存在性、唯一性以及稳定性。对于数值模拟，通过各种分数阶以图形的形式展示了近似解的行为。最后，对模拟结果进行了简要的结论讨论，以描述感染在社会中的传播动态是如何发生的。
