To study the transmission dynamic of SARS-CoV-2 using nonlinear saturated incidence rate

Kamal Shah; Thabet Abdeljawad; Rahim Ud Din

doi:10.1016/j.physa.2022.127915

To study the transmission dynamic of SARS-CoV-2 using nonlinear saturated incidence rate

Physica A. 2022 Oct 15:604:127915. doi: 10.1016/j.physa.2022.127915. Epub 2022 Jul 16.

Authors

Kamal Shah^{1

2}, Thabet Abdeljawad^{1

3}, Rahim Ud Din²

Affiliations

¹ Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia.
² Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan.
³ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.

Abstract

In this work, we construct a new SARS-CoV-2 mathematical model of SQIR type. The considered model has four compartments as susceptible $S$ , quarantine $Q$ , infected $I$ and recovered $R .$ Here saturated nonlinear incidence rate is used for the transmission of the disease. We formulate our model first and then the disease-free and endemic equilibrium (EE) are calculated. Further, the basic reproduction number is computed via the next generation matrix method. Also on using the idea of Dulac function, the global stability for the proposed model is discussed. By using the Routh-Hurwitz criteria, local stability is investigated. Through nonstandard finite difference (NSFD) scheme, numerical simulations are performed. Keeping in mind the significant importance of fractional calculus in recent time, the considered model is also investigated under fractional order derivative in Caputo sense. Finally, numerical interpretation of the model by using various fractional order derivatives are provided. For fractional order model, we utilize fractional order NSFD method. Comparison with some real data is also given.

Keywords: Basic reproduction number; Global stability; Local stability; Routh–Hurwitz criteria; SARS-Cov-2.