Okposo Newton I, Adewole Matthew O, Okposo Emamuzo N, Ojarikre Herietta I, Abdullah Farah A
Department of Mathematics, Delta State University, Abraka, PMB 1, Delta state, Nigeria.
Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Ogun State, Nigeria.
Chaos Solitons Fractals. 2021 Nov;152:111427. doi: 10.1016/j.chaos.2021.111427. Epub 2021 Sep 20.
In this work, a mathematical model consisting of a compartmentalized coupled nonlinear system of fractional order differential equations describing the transmission dynamics of COVID-19 is studied. The fractional derivative is taken in the Atangana-Baleanu-Caputo sense. The basic dynamic properties of the fractional model such as invariant region, existence of equilibrium points as well as basic reproduction number are briefly discussed. Qualitative results on the existence and uniqueness of solutions via a fixed point argument as well as stability of the model solutions in the sense of Ulam-Hyers are furnished. Furthermore, the model is fitted to the COVID-19 data circulated by Nigeria Centre for Disease Control and the two-step Adams-Bashforth method incorporating the noninteger order parameter is used to obtain an iterative scheme from which numerical results for the model can be generated. Numerical simulations for the proposed model using Adams-Bashforth iterative scheme are presented to describe the behaviors at distinct values of the fractional index parameter for of each of the system state variables. It was shown numerically that the value of fractional index parameter has a significant effect on the transmission behavior of the disease however, the infected population (the exposed, the asymptomatic infectious, the symptomatic infectious) shrinks with time when the basic reproduction number is less than one irrespective of the value of fractional index parameter.
在这项工作中，研究了一个由分数阶微分方程的分区耦合非线性系统组成的数学模型，该模型描述了新冠病毒的传播动力学。分数导数采用阿坦加纳-巴莱努-卡普托意义下的定义。简要讨论了分数模型的基本动态特性，如不变区域、平衡点的存在性以及基本再生数。通过不动点论证给出了关于解的存在性和唯一性的定性结果，以及在乌拉姆-海尔斯意义下模型解的稳定性。此外，该模型与尼日利亚疾病控制中心发布的新冠病毒数据进行拟合，并使用结合非整数阶参数的两步亚当斯-巴什福思方法来获得一个迭代方案，从中可以生成该模型的数值结果。给出了使用亚当斯-巴什福思迭代方案对所提出模型的数值模拟，以描述系统每个状态变量在分数指数参数不同值时的行为。数值结果表明，分数指数参数的值对疾病的传播行为有显著影响，然而，当基本再生数小于1时，无论分数指数参数的值如何，感染人群（暴露人群、无症状感染者、有症状感染者）都会随时间减少。
