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

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 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.

Stability analysis and comparative study on different eco‐epidemiological models: Stage structure for prey and predator concerning impulsive control

“…The solution of system ( 24) is denoted as X(t) = (P(t), T S (t), T E (t), T I (t), T N (t), N(t)) ′ and is a piecewise continuous function X ∶ R + → R 6 + therefore, X(t) is continuous in (nT, (n + 1)T], n ∈ Z + and X(nT + ) = lim t→nT + X(t) exists. Lemma 4.…”

“…2 Identifying the natural enemy of the pest and releasing the beneficial species at an early stage while the level of pests is still low is the secret to effective biological control. 3 Differential equations have been widely used as models in biology, astronomy, chemistry, engineering and other applied sciences, [4][5][6][7][8] with particular focus on population dynamics. [9][10][11][12][13] Recently, 14,15 formulated mathematical models to control Aedes aegypti mosquitoes population using biological control.…”

“…6 : The mature and immature life stages of the natural enemies is represented by N 1 (t) and N 2 (t). The growth rate of immature natural enemy population depends on mature natural enemy.…”

Computational dynamics of a fractional order substance addictions transfer model with Atangana‐Baleanu‐Caputo derivative

“…Addictions of all kinds harm people and cause a host of issues, yet understanding and dedication can help to lessen addiction. 8 In order to analyze the dynamic behavior of these problems, mathematical models play a crucial role. Tuberculosis (TB) is one of the most common causes of death in early modern societies, and it is possible that it is the captain of these dead men (as Bunyan referred to them in 1680).…”

“…The ABC-fractional derivative produces better results in many real-world problems. [12][13][14][15][16][17][18][19][20][21][22][23] Jose et al 8 developed and tested a mathematical model for SA transmission dynamics in humans in 2021. The goal of the study is to look into the effects of awareness and strong determination, two cognitive traits that have a greater impact on preventing substance abuse.…”