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Journal of Applied Nonlinear Dynamics 11(2) (2022) 427--457 | DOI:10.5890/JAND.2022.06.012

Subhashis Das$^1$, Prasenjit Mahato$^1$, Sanat Kumar Mahato$^1$, Debkumar Pal$^2$

$^1$ Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, 723104, West Bengal, India

$^2$ Chandrahati Dilip Kumar High School (H.S.), Chandrahati, 712504, West Bengal, India

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Abstract

\textbf{\textit{Background {$\&$} objectives}}\textbf{: }Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) is a highly infectious virus which causes the severe respiratory disease for human also known as Coronavirus Disease (COVID) emerged in China in December 2019 that spread rapidly all over the world. As there is no proper medicine or vaccine against the virus SARS-CoV-2 or COVID-19 to control the spread of the virus, all the countries are taking many steps as preventive measures, like lockdown, stay-at-home, social distancing, sanitization, use of mask, etc. For almost three months of lockdown many countries are relaxing the lockdown period and the movement of people. The objective of this study is to develop a new mathematical model, called the SEIQRS model in imprecise environment and to find out the essentiality of quarantine, stay-at-home orders, lockdown as precautionary measures to protect the human community. \par \textbf{\textit{Methods}}\textbf{: }In this study, after developing the COVID-19 SEIQRS model, the SEIQRS fuzzy model and the SEIQRS interval model are constructed by taking parameters as triangular fuzzy numbers and interval numbers respectively. Solution curves are drawn for two imprecise models by using MATLAB R2014a software package and the sensitivity analysis is also performed with respect to the control parameters. The next generation matrix approach is adopted to calculate the basic reproduction number ($R_0$) from the SEIQRS model to assess the transmissibility of the SARS-CoV-2. \par \textbf{\textit{Results}}\textbf{: }The basic reproduction number ($R_0$) is calculated for this model and to get the stability and disease free equilibrium the value of the basic reproduction number must be less than 1. Also, we find the solution curves in different uncertain environments and sensitivity studies show the importance of newly added population $(\alpha)$, rate of spreading asymptomatic infection $(\beta)$, rate of developing symptoms of infection $(\lambda)$, proportion of infected population in quarantine $(\gamma)$. \par \textbf{\textit{Interpretation {$\&$} conclusions}}\textbf{:} Our model shows that quarantine, lockdown are essential to control the spread of the disease as at present there is no such medicine or vaccine to combat COVID-19. Once the virus establishes transmission within the community, it will very difficult to stop the infection. As a measure of public health, healthcare and community preparedness, it would be serious to control any impending outbreak of COVID-19 in the country.

Acknowledgments

Authors are thankful to the respected referees for their constructive suggestions for the improvement of this research work. We also remain grateful to the Editor of this journal for considering our article for publication. The first and third authors would like to acknowledge the financial support by DST-INSPIRE, Government of India, Ministry of Science \& Technology, New Delhi, India (DST/INSPIRE Fellowship/2017/IF170166).

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