Sensitivity analysis-based control strategies of a mathematical model for reducing marijuana smoking

Atta Ullah; Hamzah Sakidin; Shehza Gul; Kamal Shah; Yaman Hamed; Maggie Aphane; Thabet Abdeljawad; Atta Ullah; Hamzah Sakidin; Shehza Gul; Kamal Shah; Yaman Hamed; Maggie Aphane; Thabet Abdeljawad

doi:10.3934/bioeng.2023028

AIMS Bioengineering

2023, Volume 10, Issue 4: 491-510. doi: 10.3934/bioeng.2023028

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Sensitivity analysis-based control strategies of a mathematical model for reducing marijuana smoking

1.
Mathematical and Statistical Sciences, Institute of Autonomous System, Department of Fundamental & Applied Sciences, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
3.
Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan
4.
Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 10 October 2023 Revised: 14 November 2023 Accepted: 15 November 2023 Published: 18 December 2023

The aim of the current study is to reduce marijuana use among the general population. Because marijuana is an illegal narcotic with numerous negative health effects, it continues to pose a severe threat to public health in emerging nations. In this article, a modified mathematical model of the non-users, experimental users, recreational users, and addict's (NERA) model for marijuana consumption is established by incorporating a new compartment that represents the individuals who are being moved to jail by police intervention. The overall population of humans is divided into five main components: the non-smoker's compartment, experimental smoker's compartment, recreational smoker's compartment, addicted smoker's compartment, and prisoner's compartment. The novelty of this work is to modify the NERA model for marijuana consumption and validate the modified model. Furthermore, with the help of sensitivity analysis, control strategies for marijuana consumption in the population are addressed. The invariant region and the basic reproductive number (R₀) are those parts that are needed for the validation of the proposed model. For the numerical simulation of the given model, the 4th-order Runge Kutta method will be used with the help of MATLAB to examine how the control strategies will play a role in marijuana consumption.
- marijuana,
- mathematical model,
- invariant region,
- sensitivity analysis,
- reproductive number,
- control strategies
Citation: Atta Ullah, Hamzah Sakidin, Shehza Gul, Kamal Shah, Yaman Hamed, Maggie Aphane, Thabet Abdeljawad. Sensitivity analysis-based control strategies of a mathematical model for reducing marijuana smoking[J]. AIMS Bioengineering, 2023, 10(4): 491-510. doi: 10.3934/bioeng.2023028

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Abstract

The aim of the current study is to reduce marijuana use among the general population. Because marijuana is an illegal narcotic with numerous negative health effects, it continues to pose a severe threat to public health in emerging nations. In this article, a modified mathematical model of the non-users, experimental users, recreational users, and addict's (NERA) model for marijuana consumption is established by incorporating a new compartment that represents the individuals who are being moved to jail by police intervention. The overall population of humans is divided into five main components: the non-smoker's compartment, experimental smoker's compartment, recreational smoker's compartment, addicted smoker's compartment, and prisoner's compartment. The novelty of this work is to modify the NERA model for marijuana consumption and validate the modified model. Furthermore, with the help of sensitivity analysis, control strategies for marijuana consumption in the population are addressed. The invariant region and the basic reproductive number (R₀) are those parts that are needed for the validation of the proposed model. For the numerical simulation of the given model, the 4th-order Runge Kutta method will be used with the help of MATLAB to examine how the control strategies will play a role in marijuana consumption.

Acknowledgments

The first and third authors are thankful to Universiti Teknologi PETRONAS for providing postgraduate assistantships, and Prince Sultan University is appreciated for support through TAS research lab.

Conflicts of interest

We declare that this work is original, and the content has not been published elsewhere or submitted for publication elsewhere. All the authors contributed significantly and agree with the content of the manuscript, and we declare that there is no conflict of interest in this research.

Author Contributions:

Atta Ullah: conceptualization, methodology, investigation, and visualization. Writing an original draft, reviewing, and editing; Hamzah Sakidin: supervision, conceptualization, investigation, review, and editing; Shehza Gul: conceptualization, methodology, investigation, visualization, review, and editing; Kamal Shah: supervision, conceptualization, investigation visualization, review, and editing; Yaman Hamed: supervision, conceptualization, methodology, investigation, visualization, review, and editing; Maggie Aphane: investigation, visualization, and review; Thabet Abdeljawad: investigation, visualization, and review.

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