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Discontinuity, Nonlinearity, and Complexity 11(2) (2022) 353--362 | DOI:10.5890/DNC.2022.06.014

Nita H. Shah, Ekta N. Jayswal, Ankush H. Suthar

Department of Mathematics, Gujarat University, Ahmedabad, 380009, Gujarat, India

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Abstract

The outbreak of novel coronavirus disease, namely COVID-19, has become an international public health problem in a very short period. To control the dispersal of the disease from its source, mostly all countries have restricted transportation activities as well as lockdown is implemented. This study intended to explore the effects of travel restrictions due to the outbreak of COVID-19 on air pollution. In the present work, a mathematical model has been created using two compartments lockdown and pollution. Equilibrium point and its boundedness is shown with detailed computations. The main output is computed through basic reproduction number called threshold value. With sufficient conditions, local and global stability of equilibrium points convey attention to dynamical behaviour of model. Backward bifurcation has been conducted with reference of basic reproduction number. The main objective of paper is to reduce pollution by applying optimal control strategy on lockdown. Numerical simulation and sensitivity analysis lead more light on obtained analytically results.

Acknowledgments

Authors thank reviewers for the constructive comments. All authors are thankful to DST-FIST file {\#} MSI-097 for technical support to the department of Gujarat University. Second author is funded by UGC granted National Fellowship for Other Backward Classes (NFO-2018-19-OBC-GUJ-71790) and third author is funded by a Junior Research Fellowship from the Council of Scientific & Industrial Research (file no. 09/07(0061)/2019-EMR-I).

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