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

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

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 criter...

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Main Authors: Meghadri Das, Guruprasad Samanta, Manuel De la Sen
Format: Article
Language:English
Published: MDPI AG 2021-03-01
Series:Mathematics
Subjects:
Caputo fractional differential equation
synthetic drugs
stability
optimal control
Online Access:https://www.mdpi.com/2227-7390/9/7/703
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spelling doaj-2d99fcb516784a15a09bc3952ee861b62021-03-25T00:05:04ZengMDPI AGMathematics2227-73902021-03-01970370310.3390/math9070703Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission ModelMeghadri Das0Guruprasad Samanta1Manuel De la Sen2Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, IndiaDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, IndiaInstitute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Bizkaia, SpainIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>. 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.https://www.mdpi.com/2227-7390/9/7/703Caputo fractional differential equationsynthetic drugsstabilityoptimal control
collection DOAJ
language English
format Article
sources DOAJ
author Meghadri Das
Guruprasad Samanta
Manuel De la Sen
spellingShingle Meghadri Das
Guruprasad Samanta
Manuel De la Sen
Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model
Mathematics
Caputo fractional differential equation
synthetic drugs
stability
optimal control
author_facet Meghadri Das
Guruprasad Samanta
Manuel De la Sen
author_sort Meghadri Das
title Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model
title_short Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model
title_full Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model
title_fullStr Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model
title_full_unstemmed Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model
title_sort stability analysis and optimal control of a fractional order synthetic drugs transmission model
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-03-01
description 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>. 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.
topic Caputo fractional differential equation
synthetic drugs
stability
optimal control
url https://www.mdpi.com/2227-7390/9/7/703
work_keys_str_mv AT meghadridas stabilityanalysisandoptimalcontrolofafractionalordersyntheticdrugstransmissionmodel
AT guruprasadsamanta stabilityanalysisandoptimalcontrolofafractionalordersyntheticdrugstransmissionmodel
AT manueldelasen stabilityanalysisandoptimalcontrolofafractionalordersyntheticdrugstransmissionmodel
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