The dynamics of COVID-19 with quarantined and isolation

被引:119
作者
Khan, Muhammad Altaf [1 ,2 ]
Atangana, Abdon [3 ,4 ]
Alzahrani, Ebraheem [5 ]
Fatmawati [6 ]
机构
[1] Ton Duc Thang Univ, Informetr Res Grp, Ho Chi Minh City, Vietnam
[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam
[3] Univ Free State, Fac Nat & Agr Sci, Bloemfontien, South Africa
[4] China Med Univ Hosp, Dept Med Res, Taichung, Taiwan
[5] King Abdulaziz Univ, Fac Sci, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia
[6] Univ Airlangga, Fac Sci & Technol, Dept Math, Surabaya 60115, Indonesia
关键词
COVID-19; model; Quarantine and isolation; Fractal-fractional model; Estimation of the parameters; Numerical results; MODEL;
D O I
10.1186/s13662-020-02882-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
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<approximate to>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.
引用
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页数:22
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