The dynamics of COVID-19 with quarantined and isolation

Muhammad Altaf Khan; Abdon Atangana; Ebraheem Alzahrani; Fatmawati

doi:10.1186/s13662-020-02882-9

The dynamics of COVID-19 with quarantined and isolation

Adv Differ Equ. 2020;2020(1):425. doi: 10.1186/s13662-020-02882-9. Epub 2020 Aug 14.

Authors

Muhammad Altaf Khan^{1

2}, Abdon Atangana^{3

4}, Ebraheem Alzahrani⁵, Fatmawati⁶

Affiliations

¹ Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
² Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
³ Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontien, South Africa.
⁴ Department of Medical Research, China Medical University Hospital, Taichung, Taiwan.
⁵ Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589 Saudi Arabia.
⁶ Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, 60115 Surabaya, Indonesia.

Abstract

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 $R_{0} < 1$ . 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, $R_{0} \approx 6.6361$ . 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.

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