Fractional SAQ alcohol model: stability analysis and Türkiye application
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19 sept 2024
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Categoría del artículo: Original Study
Publicado en línea: 19 sept 2024
Páginas: 125 - 136
Recibido: 12 oct 2023
Aceptado: 29 ene 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
Fig. 2
Fig. 3
Variables used in the systems and their meanings_
| Variables used in the systems | Meaning |
|---|---|
| The number of people who have not yet drunk alcohol at time |
|
| The number of individuals who consume alcohol at time |
|
| The number of individuals who have stopped drinking at time |
|
| Total population | |
The values of S, A and Q at the moment t and α = 1_
| 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_
| 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_
| 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 |
| Annual drop-off rate | |
| Annual alcohol-related death rate | |