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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

Immunity Shield Protection Mathematical Model of SARS-CoV-2 Virus Outbreak with Emphasis on Impreciseness in Terms of Intuitionistic Fuzziness

Journal of Applied Nonlinear Dynamics 12(1) (2023) 1--29 | DOI:10.5890/JAND.2023.03.001

Subhashis Das, Sanat Kumar Mahato, Prasenjit Mahato

Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal 723104, India

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Abstract

In this paper, we develop a COVID-19 mathematical model and divide the entire populations into six classes, namely susceptible, susceptible quarantined, exposed, infected, infected quarantined and recovered. We utilize the concept of ``shield immunity'' which is a different concept to herd immunity and could play a key role in getting back to normal. We consider that the recovered people are absolutely virus negative, produce antibodies to defend themselves against the virus and are able to interact with susceptible and infected people. We also assume that the recovered people may be infected when they come in contact with the infected people. Moreover, the control parameters are taken as triangular intuitionistic fuzzy numbers to incorporate the uncertainty. The model is converted to intuitionistic fuzzy model and analysed the boundedness, local and global stability, calculated the equilibrium points and basic reproduction number. We also studied optimal control of the model. The MATLAB codes are implemented to solve the system of ordinary nonlinear differential equations and to predict different scenarios for different values of the control parameters involved in the dynamical system. The sensitivities of the control parameters have also been performed to forecast the behaviour of the virus.

Acknowledgments

The authors sincerely thank to the anonymous reviewers and the editors for their valuable comments and suggestions to improve the manuscript. Authors are thankful to DST-INSPIRE, Government of India, Ministry of Science \& Technology, New Delhi, India, for financial support (DST/INSPIRE Fellowship/2017/IF170166).

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