Mathematical model with sensitivity analysis and control strategies for marijuana consumption

Abstract

The current study focuses on reducing the use of marijuana in the population. Marijuana seems to represent a serious threat to public health in developing countries since it is an illegal narcotic with various harmful health effects. The novelty of this manuscript is to modify the non-user, experimental users, recreational users, and addict's (NERA) model for marijuana consumption by incorporating a new class of addicted users under treatment, called the hospitalized class. This real-world issue is expressed in mathematical terms using first-order non-liner ordinary differential equations, and as a result, a mathematical model for marijuana consumption is established. The general population is divided into two main groups: marijuana users and non-users. Subsequently, four subgroups of abusers are created, each reflecting a different stage or degree of substance misuse. The invariant region and basic reproduction number R0 are those parts that are used for the validation of the proposed modified model and to find out the initial transmission rate of marijuana smoking in the general population, respectively. The essential factors influencing cannabis growth were identified based on the results of sensitivity analysis. Additionally, strategies were constructed in the form of prevention objectives to prevent individuals from experiencing increasing effects of marijuana. The effectiveness of these control strategies was subsequently confirmed through numerical simulations, and the numerical simulations were carried out with the help of MATLAB using the RK-4 method.

Keywords

• Dynamical system
• Control strategies
• Reproduction number
• Sensitivity Analysis
• Marijuana Consumption