STABILITY ANALYSIS OF GAMBLING BEHAVIOR MODEL WITH COGNITIVE BEHAVIORAL THERAPY TREATMENT - Asfa Niswah, Fazat; Nugraheni, Kartika; Fitria, Irma; Dewanti, Retno Wahyu (PATTIMURA UNIVERSITY, 2025)
Gambling, driven by the desire for quick profits, involves individuals or groups betting money, often resulting in significant financial consequences. Gambling behavior can be influenced by the environment or society. Thus, the dynamics of environmental influences on gambling behavior can be mathematically modeled using differential equations. This study presents a mathematical model of the environmental impact on the dynamics of the SI1I2T (Susceptible-Infective1-Infective2-Treatment) population of gamblers undergoing cognitive behavioral therapy (CBT). The model replaces the recovered sub-population with a treatment sub-population, representing individuals receiving CBT, as there is no definitive cure for gambling addiction. It consists four sub-populations: It consists of four sub-populations: (S) individuals susceptible to gambling, (I₁) gamblers who are not yet addicted, (I₂) addicted gamblers, and (T) individuals undergoing treatment but at risk of relapse. Mathematical analysis identifies two equilibrium points: a gambling-free equilibrium and an endemic gambling equilibrium. Furthermore, the results of the stability analysis using the linearization method shows that the balance point has a asymptotically stability characteristic requirement. The basic reproduction number ( ) was calculate and resulted if < 1, then the free gambler population equilibrium point is asymptotically stable, and vice versa. Based on the results of the data analysis, the value of = 0.5. This value is less than 1, so the equilibrium point obtained is the free gambler population and asymptotically stable equilibrium point. This means that the population will be free from gambling behavior. Numerical simulation represents the results of the analysis that has been obtained. Providing cognitive behavioral therapy (CBT) to gamblers in treatment can help reduce the gambler population. The population growth will decrease in such a way that it will eventually lead to a gambling-free population