Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study

Xuan Liu; Saif Ullah; Ahmed Alshehri; Mohamed Altanji

doi:10.1016/j.chaos.2021.111534

Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study

Chaos Solitons Fractals. 2021 Dec:153:111534. doi: 10.1016/j.chaos.2021.111534. Epub 2021 Nov 4.

Authors

Xuan Liu¹, Saif Ullah², Ahmed Alshehri³, Mohamed Altanji⁴

Affiliations

¹ Department of Mathematics, Hanshan Normal University, Chaozhou 515041 China.
² Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan.
³ Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
⁴ Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia.

Abstract

In this paper, a mathematical model is formulated to study the transmission dynamics of the novel coronavirus infection under the effect of treatment. The compartmental model is firstly formulated using a system of nonlinear ordinary differential equations. Then, with the help of Caputo operator, the model is reformulated in order to obtain deeper insights into disease dynamics. The basic mathematical features of the time fractional model are rigorously presented. The nonlinear least square procedure is implemented in order to parameterize the model using COVID-19 cumulative cases in Saudi Arabia for the selected time period. The important threshold parameter called the basic reproduction number is evaluated based on the estimated parameters and is found $R_{0} \approx 1.60$ . The fractional Lyapunov approach is used to prove the global stability of the model around the disease free equilibrium point. Moreover, the model in Caputo sense is solved numerically via an efficient numerical scheme known as the fractional Adamas-Bashforth-Molten approach. Finally, the model is simulated to present the graphical impact of memory index and various intervention strategies such as social-distancing, disinfection of the virus from environment and treatment rate on the pandemic peaks. This study emphasizes the important role of various scenarios in these intervention strategies in curtailing the burden of COVID-19.

Keywords: COVID-19 mathematical model; Caputo derivative; Numerical simulations; Parameter estimation; Real incidence data.