Mathematical Model of Drinking Epidemic

Adu, Isaac Kwasi; Osman, Mojeeb AL-Rahman EL-Nor; Chen, Yang

doi:10.9734/bjmcs/2017/33659

Cited by 21 publications

(16 citation statements)

References 12 publications

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“…[21][22][23] In terms of alcohol, numerous statistical models have been developed and studied in order to further reduce the number of drinkers. 24,25 As well as the best of our knowledge, relatively few scientific articles on substance addictions have been written. In order to model the dynamics of addiction behaviour, the majority of the models have taken into account of compartmental modeling approach used in modeling of infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

Impact of strong determination and awareness on substance addictions: A mathematical modeling approach

Jose

Raja

Zhu

et al. 2021

Math Methods in App Sciences

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Substance addiction such as tobacco, alcohol, opioids, drug addiction and so on are increasing day by day. Awareness about the harmful effects of substance addiction on health and strong will power of people to get rid of the addiction have positive impact on controlling substance addiction. The aim of this research is to examine the impact of awareness and strong determination, the two cognitive factors that have greater impact in preventing substance addiction. Addiction adversely affects self‐efficacy of younger generation, thought processing, metabolisms in human body, psychosocial effects and cardiovascular diseases. In this paper, we have developed a mathematical model regarding substance addiction. It consist of six compartments namely, susceptible class, light substance addict class, risk substance addict class, potential substance addict class, rehabilitation class and quitter class. The substance addiction generation number false(scriptRAfalse) has been determined, and the model is locally asymptotically stable at substance addictions free equilibrium point (SAFEP) scriptD∘ when scriptRA<1. It is found that, when scriptRA=1, a backward bifurcation can occur and when scriptRA>1, the substance addictions persistent equilibrium point (SAPEP) scriptD⋆ becomes stable. Further analysis gives the global asymptotic stability of SAFEP. An application of this model, smoking model, is explored. Smoking model gives a different comparative study which proves the relevance and the importance of our model. We get a clear idea about smokers' behaviour at different stages of high determination and knowledge and also establish the relationship between scriptRA and these parameters. Finally, we give some recommendations for preventing addiction which can be implemented in society.

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Section: Introductionmentioning

confidence: 99%

Impact of strong determination and awareness on substance addictions: A mathematical modeling approach

Jose

Raja

Zhu

et al. 2021

Math Methods in App Sciences

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“…It is seen that the use as an infectious disease spreads in society. In this study, we created the mathematical model of alcohol use considering the SIR model of epidemic diseases [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model

Tarakçi

Gözükızıl

2021

Sakarya University Journal of Science

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This paper is devoted to studying the mathematical model of the alcohol-consuming population. For this purpose, the formulation of the model including the alcohol-consuming population is presented; then the balance points related to non-alcohol use and positive alcohol use are discussed. Hurwitz theorem is used to find the local stability of the model, and Lyapunov function theory is used to investigate the global stability. The same mathematical model with alcohol use is considered for Sakarya and Turkey, individual numerical results are presented, and stability analyzes are examined. Finally, using the numerical data, a simulation is made in Matlab with the Runge-Kutta fourth-order method.

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“…Huo and Song [7] divided heavy drinkers in their study into two types: those who confess drinking and those who do not, and they proposed a two-stage model for binge drinking problem taking into consideration the transition of drinkers from the class of susceptible individuals towards the class of admitting drinkers. Adu et al [8] used a nonlinear SHTR mathematical model to study the dynamics of drinking epidemic; they divided their population into four classes: nondrinkers (S), heavy drinkers (H), drinkers receiving treatment (T), and recovered drinkers (R). ey discussed the existence and stability of drinking-free and endemic equilibrium.…”

Section: Introductionmentioning

confidence: 99%

A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control

Khajji

Labzai

Kouidere

et al. 2020

Journal of Applied Mathematics

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In this paper, we propose a discrete mathematical model that describes the interaction between the classes of drinkers, namely, potential drinkers P, moderate drinkers M, heavy drinkers H, poor heavy drinkers Tp, rich heavy drinkers Tr, and quitters of drinking Q. We also focus on the importance of treatment within addiction treatment centers aiming to find the optimal strategies to minimize the number of drinkers and maximize the number of heavy drinkers who join addiction treatment centers. We use three controls which represent awareness programs through media and education for the potential drinkers, efforts to encourage the heavy drinkers to join addiction treatment centers, and psychological support with follow-up for the individuals who quit drinking. We use Pontryagin’s maximum principle in discrete time to characterize these optimal controls. The resulting optimality system is solved numerically by Matlab. Consequently, the obtained results confirm the performance of the optimization strategy.

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Mathematical Model of Drinking Epidemic

Cited by 21 publications

References 12 publications

Impact of strong determination and awareness on substance addictions: A mathematical modeling approach

Impact of strong determination and awareness on substance addictions: A mathematical modeling approach

Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model

A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control

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