Mathematical analysis of COVID-19 via new mathematical model

Abdullah; Saeed Ahmad; Saud Owyed; Abdel-Haleem Abdel-Aty; Emad E Mahmoud; Kamal Shah; Hussam Alrabaiah

doi:10.1016/j.chaos.2020.110585

Mathematical analysis of COVID-19 via new mathematical model

Chaos Solitons Fractals. 2021 Feb:143:110585. doi: 10.1016/j.chaos.2020.110585. Epub 2020 Dec 26.

Authors

Abdullah¹, Saeed Ahmad¹, Saud Owyed², Abdel-Haleem Abdel-Aty^{3

4}, Emad E Mahmoud^{5

6}, Kamal Shah¹, Hussam Alrabaiah^{7

8}

Affiliations

¹ Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi Arabia.
³ Department of Physics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi Arabia.
⁴ Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.
⁵ Department of Mathematics and Statistics, College of Science, Taif University, PO Box 11099, Taif 21944, Saudi Arabia.
⁶ Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
⁷ College of Engineering, Al Ain University, Al Ain, United Arab Emirates.
⁸ Department of Mathematics, Tafila Technical University, Tafila, Jordan.

Abstract

We develop a new mathematical model by including the resistive class together with quarantine class and use it to investigate the transmission dynamics of the novel corona virus disease (COVID-19). Our developed model consists of four compartments, namely the susceptible class, $S (t),$ the healthy (resistive) class, $H (t),$ the infected class, $I (t)$ and the quarantine class, $Q (t)$ . We derive basic properties like, boundedness and positivity, of our proposed model in a biologically feasible region. To discuss the local as well as the global behaviour of the possible equilibria of the model, we compute the threshold quantity. The linearization and Lyapunov function theory are used to derive conditions for the stability analysis of the possible equilibrium states. We present numerical simulations to support our investigations. The simulations are compared with the available real data for Wuhan city in China, where the infection was initially originated.

Keywords: Basic reproduction number; COVID 19; Linearization theory; Lyapunov function; Mathematical model; Numerical simulations; Stability analysis.