An analysis of a nonlinear susceptible-exposed-infected-quarantine-recovered pandemic model of a novel coronavirus with delay effect

Ali Raza; Ali Ahmadian; Muhammad Rafiq; Soheil Salahshour; Massimiliano Ferrara

doi:10.1016/j.rinp.2020.103771

An analysis of a nonlinear susceptible-exposed-infected-quarantine-recovered pandemic model of a novel coronavirus with delay effect

Results Phys. 2021 Feb:21:103771. doi: 10.1016/j.rinp.2020.103771. Epub 2020 Dec 28.

Authors

Ali Raza¹, Ali Ahmadian^{2

3

4}, Muhammad Rafiq⁵, Soheil Salahshour⁶, Massimiliano Ferrara^{3

7}

Affiliations

¹ Department of Mathematics, National College of Business Administration and Economics Lahore, Pakistan.
² Institute of Visual Informatics, National University of Malaysia, 43600 UKM, Bangi, Selangor, Malaysia.
³ Department of Law, Economics and Human Sciences& Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy.
⁴ School of Mathematical Sciences, College of Science and Technology, Wenzhou-Kean University, Wenzhou, China.
⁵ Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan.
⁶ Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey.
⁷ ICRIOS-The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship, Bocconi University, Department of Management and Technology Via Sarfatti, 25 20136 Milano MI, Italy.

Abstract

In the present study, a nonlinear delayed coronavirus pandemic model is investigated in the human population. For study, we find the equilibria of susceptible-exposed-infected-quarantine-recovered model with delay term. The stability of the model is investigated using well-posedness, Routh Hurwitz criterion, Volterra Lyapunov function, and Lasalle invariance principle. The effect of the reproduction number on dynamics of disease is analyzed. If the reproduction number is less than one then the disease has been controlled. On the other hand, if the reproduction number is greater than one then the disease has become endemic in the population. The effect of the quarantine component on the reproduction number is also investigated. In the delayed analysis of the model, we investigated that transmission dynamics of the disease is dependent on delay terms which is also reflected in basic reproduction number. At the end, to depict the strength of the theoretical analysis of the model, computer simulations are presented.

Keywords: Computer simulations; Coronavirus; Nonlinear delay pandemic model; Reproduction number; Stability.