The dynamics of COVID-19 with quarantined and isolation

Advances in Difference Equations

article

Khan, Muhammad Altaf¹  Atangana, Abdon³  Alzahrani, Ebraheem⁵  Fatmawati⁶ 

[1] Informetrics Research Group, Ton Duc Thang University;Faculty of Mathematics and Statistics, Ton Duc Thang University;Faculty of Natural and Agricultural Sciences, University of the Free State;Department of Medical Research, China Medical University Hospital;Department of Mathematics, Faculty of Science, King Abdulaziz University;Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga

关键词: COVID-19 model;    Quarantine and isolation;    Fractal-fractional model;    Estimation of the parameters;    Numerical results;   

DOI  :  10.1186/s13662-020-02882-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In the present paper, we formulate a new mathematical model for the dynamics of COVID-19 with quarantine and isolation. Initially, we provide a brief discussion on the model formulation and provide relevant mathematical results. Then, we consider the fractal-fractional derivative in Atangana–Baleanu sense, and we also generalize the model. The generalized model is used to obtain its stability results. We show that the model is locally asymptotically stable if R0 < 1. Further, we consider the real cases reported in China since January 11 till April 9, 2020. The reported cases have been used for obtaining the real parameters and the basic reproduction number for the given period, R0 ≈ 6.6361. The data of reported cases versus model for classical and fractal-factional order are presented. We show that the fractal-fractional order model provides the best fitting to the reported cases. The fractional mathematical model is solved by a novel numerical technique based on Newton approach, which is useful and reliable. A brief discussion on the graphical results using the novel numerical procedures are shown. Some key parameters that show significance in the disease elimination from the society are explored.

【 授权许可】

CC BY