A mathematical model with control strategies for marijuana smoking prevention

Atta Ullah; Hamzah Sakidin; Kamal Shah; Yaman Hamed; Thabet Abdeljawad; Atta Ullah; Hamzah Sakidin; Kamal Shah; Yaman Hamed; Thabet Abdeljawad

doi:10.3934/era.2024107

Electronic Research Archive

2024, Volume 32, Issue 4: 2342-2362. doi: 10.3934/era.2024107

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Research article

A mathematical model with control strategies for marijuana smoking prevention

1.
Mathematical and Statistical Sciences, Institute of Autonomous System, Department of Fundamental & Applied Sciences, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak, 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 Medical Research, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 21 December 2023 Revised: 05 March 2024 Accepted: 07 March 2024 Published: 22 March 2024

Our goal of this study is to prevent marijuana smoking in the human population. In this manuscript, an updated mathematical model was established by incorporating two additional compartments: The hospitalized class and the prisoner's class. The updated model was validated, and it was shown to be novel compared to the non-user, experimental, recreational, and addicted (NERA) users' model. This distinction was crucial as it was challenging to prevent marijuana usage without these realistic classes. The entire population was split into six primary groups, including these new classes: non-users, experimental, recreational, addicted, hospitalized, and prisoners' class. Additionally, control techniques for marijuana prevention in the population were addressed with the aid of sensitivity analysis. The important point at which we may have determined the preliminary transmission rate of marijuana smoking was the basic reproductive number $ {\mathbb{R}}_{0} $. Utilizing MATLAB, the Runge-Kutta method of order four was employed for the numerical simulation of the updated model to investigate the impact of control measures on marijuana smoking prevention.
- mathematical model,
- marijuana prevention,
- reproduction number,
- sensitivity analysis,
- control strategies
Citation: Atta Ullah, Hamzah Sakidin, Kamal Shah, Yaman Hamed, Thabet Abdeljawad. A mathematical model with control strategies for marijuana smoking prevention[J]. Electronic Research Archive, 2024, 32(4): 2342-2362. doi: 10.3934/era.2024107

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Abstract

Our goal of this study is to prevent marijuana smoking in the human population. In this manuscript, an updated mathematical model was established by incorporating two additional compartments: The hospitalized class and the prisoner's class. The updated model was validated, and it was shown to be novel compared to the non-user, experimental, recreational, and addicted (NERA) users' model. This distinction was crucial as it was challenging to prevent marijuana usage without these realistic classes. The entire population was split into six primary groups, including these new classes: non-users, experimental, recreational, addicted, hospitalized, and prisoners' class. Additionally, control techniques for marijuana prevention in the population were addressed with the aid of sensitivity analysis. The important point at which we may have determined the preliminary transmission rate of marijuana smoking was the basic reproductive number $ {\mathbb{R}}_{0} $. Utilizing MATLAB, the Runge-Kutta method of order four was employed for the numerical simulation of the updated model to investigate the impact of control measures on marijuana smoking prevention.

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