Li Xiao-Ping, DarAssi Mahmoud H, Khan Muhammad Altaf, Chukwu C W, Alshahrani Mohammad Y, Shahrani Mesfer Al, Riaz Muhammad Bilal
School of Mathematics and Information Science, Xiangnan University, Chenzhou, 423000, Hunan, PR China.
Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, Jordan.
Results Phys. 2022 Jul;38:105652. doi: 10.1016/j.rinp.2022.105652. Epub 2022 May 30.
We consider a new mathematical model for the COVID-19 disease with Omicron variant mutation. We formulate in details the modeling of the problem with omicron variant in classical differential equations. We use the definition of the Atangana-Baleanu derivative and obtain the extended fractional version of the omicron model. We study mathematical results for the fractional model and show the local asymptotical stability of the model for infection-free case if . We show the global asymptotically stable of the model for the disease free case when . We show the existence and uniqueness of solution of the fractional model. We further extend the fractional order model into piecewise differential equation system and give a numerical algorithm for their numerical simulation. We consider the real cases of COVID-19 in South Africa of the third wave March 2021-Sep 2021 and estimate the model parameters and get . The real parameters values are used to show the graphical results for the fractional and piecewise model.
我们考虑一个针对具有奥密克戎变体突变的新冠疾病的新数学模型。我们在经典微分方程中详细阐述了奥密克戎变体问题的建模。我们使用阿坦加纳 - 巴莱亚努导数的定义，得到了奥密克戎模型的扩展分数阶版本。我们研究了分数阶模型的数学结果，并表明在 时无感染情况下模型的局部渐近稳定性。当 时，我们证明了疾病无感染情况下模型的全局渐近稳定性。我们证明了分数阶模型解的存在性和唯一性。我们进一步将分数阶模型扩展为分段微分方程组，并给出了用于其数值模拟的数值算法。我们考虑了2021年3月至2021年9月南非第三波新冠疫情的实际病例，估计了模型参数并得到 。使用实际参数值展示了分数阶模型和分段模型的图形结果。
