Page 48 - IJOCTA-15-3

M. Aychluh et.al. / IJOCTA, Vol.15, No.3, pp.407-425 (2025)
have a significant impact on the system results. gambling frequently. For a few weeks, they will
gamble with no problem but may show signs of
200
γ 1 = 0.2 γ 1 = 0.4 γ 1 = 0.6 γ 1 = 0.8
addiction and will move to the addiction stage.
Figures 8-9 confirm the behavior of no problem
150
gamblers and minor-risk under varying fractional
N (t) 100 order values. Due to several factors, peaceful
gambling can transition into excessive gambling
activities.
50

0 70
0 20 40 60 80 100 υ = 0.25 υ = 0.35 υ = 0.45 υ = 0.55 υ = 0.65
t
60
Figure 6. The approximate solutions of N(t) with 50
different values γ 1 when υ = 0.95 40
M (t)
Figure 6 examines how the parameter γ 1 (weight 30
of non-problem gamblers A on no gamblers N) 20
affects the solution N(t) with time intervals.
Higher γ 1 (e.g., γ 1 = 0.8) accelerates the de- 10
cline of N(t), as more individuals transition 0
to start gambling. Conversely, lower γ 1 (e.g., 0 20 40 60 80 100
t
γ 1 = 0.2) slows the decline, reducing recruitment
into gambling activities. Public awareness cam-
Figure 9. The approximate solutions of M(t) with
paigns (reducing γ 1 ) could slow gambling uptake. different fractional order values
200
γ 2 = 0.3 γ 2 = 0.5 γ 2 = 0.7 γ 2 = 0.9 120
ς = 0.5 ς = 0.1 ς = 0.05 ς = 0.01 ς = 0.005
150 100

N (t) 100 80
M (t) 60

50
40
0
0 10 20 30 40 50 60 70 80 90 100 20
t
0
Figure 7. The approximate solutions of N(t) with 0 20 40 60 80 100
different values γ 2 when υ = 0.95 t
Figure 7 tests the impact of γ 2 , which Figure 10. The approximate solutions of M(t) with
different values of recovery rate ς when υ = 0.5
is the influence of minor-risk gamblers.
Early intervention for minor-risk gamblers
may indirectly protect the new gamblers.
Figure 10 evaluates how the recovery rate ς
250 (transition from M to R) affects M(t). Higher
υ = 0.25 υ = 0.45 υ = 0.65 υ = 0.85
recovery rate (e.g., ς = 0.5) rapidly reduces M(t),
200
as more quit gambling. Lower recovery rate (e.g.,
150 ς = 0.005) increases the risk of gambling in
A(t) the population. Strengthening recovery programs
100
(e.g., counseling, religion activities) reduces the
risks of gamblers. Early decision to stop daily
50
gambling is highly recommended, especially for
0 young gamblers. Numerical results of the behav-
0 20 40 60 80 100
t ior of minor risk gamblers in relation to the re-
covery parameter ς are shown in Figure 10. It is
Figure 8. The approximate solutions of A(t) with
clearly visible that as the recovery rate ς increases
different fractional order values
from 0.005 to 0.5, the number of individuals in the
Some non-problem gamblers may show interest in risk gambling stage decreases.
420