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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Transmission Dynamics and Control of COVID-19: A Mathematical Modelling Study

Journal of Applied Nonlinear Dynamics 12(2) (2023) 405--425 | DOI:10.5890/JAND.2023.06.015

Kalyan Das$^1$, M. N. Srinivas${}^{2} $, Pabel Shahrear${}^{3} $, S. M. Saydur Rahman${}^{3 }$, Md M.H. Nahid${}^{4 }$, B. S. N. Murthy$ {}^{5} $

${}^{1 }$ Department of Basic and Applied Sciences, National Institute of Food Technology Entrepreneurship and Management, HSIIDC Industrial Estate, Kundli-131028, Haryana, India

${}^{2 }$ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, India

${}^{ 3 }$ Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, Bangladesh

${}^{4}$ Department of Computer Science and Engineering, Shahjalal University of Science and Technology, Sylhet, $ Department of Mathematics, Aditya College of Engineering and Technology, JNTUK, Andhrapradesh, India

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Abstract

We look at the SQIRP mathematical model for new coronavirus transmission in Bangladesh and India in this study. The basic reproduction number of the SQIRP system is designed using the next cohort matrix process. The SQIRP system has asymptotically stable locally at an infection-free equilibrium point when the basic reproduction number is not more than unity and unsteady when the value is greater than unity. The SQIRP system is found to go through a backward bifurcation, which is a novel perspective for Coronavirus infection transmission. The infection-free equilibrium and endemic equilibrium are shown to be asymptotically stable globally using the Lyapunov function hypothesis and the invariance principle of Lasalle. A SQIRP system with backward bifurcation is explored using stochastic analysis. The ecological stochasticity in the appearance of white noise best describes the system's value. To verify the results, more numerical simulations are run.

Acknowledgments

The Department of Basic and Applied Sciences, NIFTEM, NIFTEM Knowledge Centre, and the Department of Mathematics, Vellore Institute of Technology are greatly acknowledged. It has been supported partially by the SUST Research Centre, Shahjalal University of Science and Technology, Sylhet 3114, Bangladesh, through research funds PS/2020/1/25 and PS/2021/1/17.

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