Department of Mathematics, City University of Science and Information Technology, Khyber Pakhtunkhwa, Peshawar, 25000, Pakistan.
Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam.
Sci Rep. 2020 Dec 17;10(1):22268. doi: 10.1038/s41598-020-79405-9.
Recently, novel coronavirus is a serious global issue and having a negative impact on the economy of the whole world. Like other countries, it also effected the economy and people of Pakistan. According to the publicly reported data, the first case of novel corona virus in Pakistan was reported on 27th February 2020. The aim of the present study is to describe the mathematical model and dynamics of COVID-19 in Pakistan. To investigate the spread of coronavirus in Pakistan, we develop the SEIR time fractional model with newly, developed fractional operator of Atangana-Baleanu. We present briefly the analysis of the given model and discuss its applications using world health organization (WHO) reported data for Pakistan. We consider the available infection cases from 19th March 2020, till 31st March 2020 and accordingly, various parameters are fitted or estimated. It is worth noting that we have calculated the basic reproduction number [Formula: see text] which shows that virus is spreading rapidly. Furthermore, stability analysis of the model at disease free equilibrium DFE and endemic equilibriums EE is performed to observe the dynamics and transmission of the model. Finally, the AB fractional model is solved numerically. To show the effect of the various embedded parameters like fractional parameter [Formula: see text] on the model, various graphs are plotted. It is worth noting that the base of our investigation, we have predicted the spread of disease for next 200 days.
最近，新型冠状病毒是一个严重的全球问题，对全世界的经济产生了负面影响。和其他国家一样，它也影响了巴基斯坦的经济和人民。据公开报道，巴基斯坦首例新型冠状病毒病例于 2020 年 2 月 27 日报告。本研究的目的是描述 COVID-19 在巴基斯坦的数学模型和动力学。为了研究冠状病毒在巴基斯坦的传播，我们开发了具有 Atangana-Baleanu 新开发的分数算子的 SEIR 时间分数模型。我们简要介绍了所给模型的分析，并使用世界卫生组织（WHO）报告的巴基斯坦数据讨论了其应用。我们考虑了从 2020 年 3 月 19 日到 2020 年 3 月 31 日的可用感染病例，并相应地拟合或估计了各种参数。值得注意的是，我们已经计算了基本繁殖数[公式：见文本]，这表明病毒传播迅速。此外，还对无病平衡点 DFE 和地方病平衡点 EE 处模型的稳定性进行了分析，以观察模型的动态和传播。最后，对 AB 分数模型进行了数值求解。为了显示分数参数[公式：见文本]等各种嵌入参数对模型的影响，绘制了各种图形。值得注意的是，我们的研究基础是预测未来 200 天疾病的传播。
