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Fractional SAQ alcohol model: stability analysis and Türkiye application

Zafer Öztürk

Zafer Öztürk

Department of Mathematics, Faculty of Science and Arts, Nevşehir Hacı Bektaş Veli UniversityNevşehir, Türkiye
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Öztürk, Zafer
, 
Halis Bilgil

Halis Bilgil

Engineering Basic Sciences, Faculty of Engineering Architecture and Design, Kayseri UniversityKayseri, Türkiye
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Bilgil, Halis
 e 
Sezer Sorgun

Sezer Sorgun

Department of Mathematics, Faculty of Science and Arts, Nevşehir Hacı Bektaş Veli UniversityNevşehir, Türkiye
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Sorgun, Sezer
  
19 set 2024
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Categoria dell'articolo: Original Study
Pubblicato online: 19 set 2024
Pagine: 125 - 136
Ricevuto: 12 ott 2023
Accettato: 29 gen 2024
DOI: https://doi.org/10.2478/ijmce-2025-0011
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© 2025 Zafer Öztürk et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

The graph of change of the S compartment model.
The graph of change of the S compartment model.

Fig. 2

The graph of change of the A compartment model.
The graph of change of the A compartment model.

Fig. 3

The graph of change of the Q compartment model.
The graph of change of the Q compartment model.

Variables used in the systems and their meanings_

Variables used in the systems Meaning
S(t) The number of people who have not yet drunk alcohol at time t
A(t) The number of individuals who consume alcohol at time t
Q(t) The number of individuals who have stopped drinking at time t
N(t) Total population

The values of S, A and Q at the moment t and α = 1_

t S(t) A(t) Q(t)
0 47236000,00 13324075,00 111914,00
1 48020534,09 11847377,52 1255322,34
2 48788026,96 10534374,94 2246579,71
3 49538833,66 9366916,98 3103111,20
4 50273303,06 8328866,40 3840397,62
5 50991777,89 7405875,67 4472191,38
6 51694594,77 6585188,43 5010708,48
7 52382084,20 5855462,94 5466799,10
8 53054570,66 5206615,18 5850099,33
9 53712372,62 4629679,34 6169166,05
10 54355802,55 4116683,74 6431596,82
11 54985167,05 3660540,64 6644136,49
12 55600766,82 3254948,13 6812771,99
13 56202896,76 2894303,02 6942816,54
14 56791846,02 2573623,34 7038984,64

The values of S, A and Q at the moment t and α = 0_9_

t S(t) A(t) Q(t)
0 47236000,00 13324075,00 111914,00
1 48051719,30 11788678,83 1300772,80
2 48849015,86 10430249,76 2325144,23
3 49628288,72 9228385,98 3204614,99
4 50389929,72 8165038,40 3956499,44
5 51134323,51 7224239,19 4596101,97
6 51861847,62 6391861,78 5136949,05
7 52572872,46 5655408,44 5590994,60
8 53267761,39 5003822,41 5968801,52
9 53946870,75 4427321,72 6279702,46
10 54610549,93 3917252,16 6531941,87
11 55259141,43 3465957,24 6732801,78
12 55892980,89 3066663,10 6888713,00
13 56512397,21 2713376,78 7005353,54
14 57117712,58 2400796,14 7087735,66

The values of S, A and Q at the moment t and α = 0_8_

t S(t) A(t) Q(t)
0 47236000,00 13324075,00 111914,00
1 48078330,74 11738589,18 1339557,26
2 48901017,27 10341805,13 2391805,87
3 49704498,93 9111258,54 3290226,66
4 50489206,87 8027160,15 4053802,80
5 51255564,10 7072077,09 4699241,80
6 52003985,50 6230652,22 5241246,87
7 52734877,91 5489356,88 5692755,89
8 53448640,12 4836273,14 6065151,96
9 54145663,01 4260901,95 6368448,88
10 54826329,51 3753994,17 6611454,43
11 55491014,77 3307401,73 6801914,37
12 56140086,16 2913946,51 6946639,11
13 56773903,38 2567304,87 7051615,42
14 57392818,59 2261905,86 7122104,73

Parameters and their meanings_

Parameters Meaning
β Annual rate of alcohol initiation
µ Annual birth and death rate
m Annual drop-off rate
w Annual alcohol-related death rate
Lingua:
Inglese
Frequenza di pubblicazione:
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