Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model

Meghadri Das, Guruprasad Samanta and Manuel De la Sen
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Meghadri Das: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
Guruprasad Samanta: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
Manuel De la Sen: Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Spain

Mathematics, 2021, vol. 9, issue 7, 1-34

Abstract: In this work, a fractional-order synthetic drugs transmission model with psychological addicts has been proposed along with psychological treatment. The effects of synthetic drugs are deadly and sometimes even violent. We have studied the local and global stability of the model with different criterion. The existence and uniqueness criterion along with positivity and boundedness of the solutions have also been established. The local and global stabilities are decided by the basic reproduction number R 0 . We have also analyzed the sensitivity of parameters. An optimal control problem has been formulated by controlling psychological addiction and analyzed by the help of Pontryagin maximum principle. These results are verified by numerical simulations.

Keywords: Caputo fractional differential equation; synthetic drugs; stability; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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