Naik Parvaiz Ahmad, Yavuz Mehmet, Qureshi Sania, Zu Jian, Townley Stuart
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi People's Republic of China.
Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090 Konya, Turkey.
Eur Phys J Plus. 2020;135(10):795. doi: 10.1140/epjp/s13360-020-00819-5. Epub 2020 Oct 8.
Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the virus is not yet known. The outbreak has caused pandemic with 26,622,706 confirmed infections and 874,708 reported deaths worldwide till August 31, 2020, with 17,717,911 recovered cases. Currently, there exist no vaccines officially approved for the prevention or management of the disease, but alternative drugs meant for HIV, HBV, malaria and some other flus are used to treat this virus. In the present paper, a fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana-Baleanu-Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed. The reproduction number is obtained for the prediction and persistence of the disease. The dynamic behavior of the equilibria is studied by using fractional Routh-Hurwitz stability criterion and fractional La Salle invariant principle. Special attention is given to the global dynamics of the equilibria. Moreover, the fitting of parameters through least squares curve fitting technique is performed, and the average absolute relative error between COVID-19 actual cases and the model's solution for the infectious class is tried to be reduced and the best fitted values of the relevant parameters are achieved. The numerical solution of the proposed COVID-19 fractional-order model under the Caputo operator is obtained by using generalized Adams-Bashforth-Moulton method, whereas for the Atangana-Baleanu-Caputo operator, we have used a new numerical scheme. Also, the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals. Furthermore, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary-order derivative.
冠状病毒是一大类病毒，可引发从普通感冒到严重呼吸窘迫等不同症状，且可见于骆驼、牛、猫和蝙蝠等不同种类的动物。名为COVID - 19的新型冠状病毒是一种新出现的病毒，已在世界许多国家出现，但该病毒的实际来源尚不清楚。此次疫情已造成全球大流行，截至2020年8月31日，全球确诊感染病例达26622706例，报告死亡病例874708例，康复病例17717911例。目前，尚无正式批准用于预防或治疗该疾病的疫苗，但用于治疗艾滋病病毒、乙肝病毒、疟疾和其他一些流感的替代药物被用于治疗这种病毒。在本文中，提出并分析了一个用于COVID - 19疫情传播的分数阶流行病模型，该模型采用了两种不同的算子，即经典的卡普托算子和阿坦加纳 - 巴莱亚努 - 卡普托算子。得到了用于疾病预测和持续存在的基本再生数。利用分数阶劳斯 - 赫尔维茨稳定性判据和分数阶拉萨尔不变原理研究了平衡点的动态行为。特别关注了平衡点的全局动态。此外，通过最小二乘曲线拟合技术进行参数拟合，试图降低COVID - 19实际病例与模型中感染类别的解之间的平均绝对相对误差，并获得相关参数的最佳拟合值。采用广义亚当斯 - 巴什福思 - 莫尔顿方法获得了卡普托算子下所提出的COVID - 19分数阶模型的数值解，而对于阿坦加纳 - 巴莱亚努 - 卡普托算子，我们使用了一种新的数值格式。此外，在总体中纳入了治疗 compartment，以确定用于治疗感染个体的替代药物的影响。此外，对模型进行了数值模拟及其图形展示，以直观呈现我们理论结果的有效性，并监测任意阶导数的影响。
