Impact of strong determination and awareness on substance addictions: A mathematical modeling approach. (29th October 2021)

• Record Type: Journal Article
• Authors: Jose, Sayooj Aby; Raja, Ramachandran; Zhu, Quanxin; Alzabut, Jehad; Niezabitowski, Michal; Balas, Valentina E.
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 8(2022)
• Page Start: 4140
• Page End: 4160
• Publication Date: 2021-10-29
• Subjects: forward and backward bifurcations -- local and global stability -- mathematical modeling -- smoking model -- substance addiction generation number -- substance addictions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7859
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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 ( R A ) has been determined, and the model is locally asymptotically stable at substance addictions free equilibrium point (SAFEP) D ∘ when R A < 1 . It is found that, when R A = 1, a backward bifurcation can occur and when R A > 1, the substance addictions persistent equilibrium point (SAPEP) D ⋆ 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 R A and these parameters. Finally, we give some recommendations for preventing addiction which can be implemented in society.