Fractional SAQ alcohol model: stability analysis and Türkiye application

[1]Adu I.K., Osman M.A.R.E.N., Yang C., Mathematical model of drinking epidemic, Journal of Advances in Mathematics and Computer Science, 22(5), 1–10, 2017. AduI.K. OsmanM.A.R.E.N. YangC. Mathematical model of drinking epidemic Journal of Advances in Mathematics and Computer Science 22 5 1 10 2017Search in Google Scholar

[2]Khajji B., Labzai A., Balatif O., Rachik M., Mathematical modeling and analysis of an alcohol drinking model with the influence of alcohol treatment centers, International Journal of Mathematics and Mathematical Sciences, 2020(ID: 4903168), 1–12, 2020. KhajjiB. LabzaiA. BalatifO. RachikM. Mathematical modeling and analysis of an alcohol drinking model with the influence of alcohol treatment centers International Journal of Mathematics and Mathematical Sciences 2020 (ID: 4903168) 1 12 2020 Search in Google Scholar

[3]Sharomi O., Gumel A.B., Curtailing smoking dynamics: a mathematical modeling approach, Applied Mathematics and Computation, 195(2), 475–499, 2008. SharomiO. GumelA.B. Curtailing smoking dynamics: a mathematical modeling approach Applied Mathematics and Computation 195 2 475 499 2008Search in Google Scholar

[4]Podlubny I., Fractional Differential Equations, Academy Press, San Diego, California, USA, 1999. PodlubnyI. Fractional Differential Equations Academy Press San Diego, California, USA 1999 Search in Google Scholar

[5]Ertürk V.S., Zaman G., Momani S., A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives, Computers and Mathematics with Applications, 64(10), 3065–3074, 2012. ErtürkV.S. ZamanG. MomaniS. A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives Computers and Mathematics with Applications 64 10 3065 3074 2012Search in Google Scholar

[6]Allen L.J.S., An Introduction to Mathematical Biology, Pearson/Prentice Hall, USA, 2007. AllenL.J.S. An Introduction to Mathematical Biology Pearson/Prentice Hall USA 2007 Search in Google Scholar

[7]Driessche P.V.D., Watmough J., Reproduction numbers and sub-threshold endemic equilibria for compartmental model of disease transmission, Mathematical Biosciences, 180(1–2), 29–48, 2002. DriesscheP.V.D. WatmoughJ. Reproduction numbers and sub-threshold endemic equilibria for compartmental model of disease transmission Mathematical Biosciences 180 1–2 29 48 2002 Search in Google Scholar

[8]Öztürk Z., Bilgil H., Sorgun S., Application of fractional SIQRV model for SARS-CoV-2 and stability analysis, Symmetry, 15(5), 1048, 2023. ÖztürkZ. BilgilH. SorgunS. Application of fractional SIQRV model for SARS-CoV-2 and stability analysis Symmetry 15 5 1048 2023 Search in Google Scholar

[9]Yousef A., Bozkurt F., Abdeljawad T., Qualitative analysis of a fractional pandemic spread model of the novel coronavirus (COVID-19), Computers Materials and Continua, 66(1), 843–869, 2020. YousefA. BozkurtF. AbdeljawadT. Qualitative analysis of a fractional pandemic spread model of the novel coronavirus (COVID-19) Computers Materials and Continua 66 1 843 869 2020Search in Google Scholar

[10]Owolabi K.M., Shikongo A., Fractal fractional operator method on HER2+ breast cancer dynamics, International Journal of Applied and Computational Mathematics, 7(3), 85, 2021. OwolabiK.M. ShikongoA. Fractal fractional operator method on HER2+ breast cancer dynamics International Journal of Applied and Computational Mathematics 7 3 85 2021 Search in Google Scholar

[11]Karaagac B., Owolabi K.M., Nisar K.S., Analysis and dynamics of illicit drug use described by fractional derivative with Mittag-Leffler kernel, Computers Materials and Continua, 65(3), 1905–1924, 2020. KaraagacB. OwolabiK.M. NisarK.S. Analysis and dynamics of illicit drug use described by fractional derivative with Mittag-Leffler kernel Computers Materials and Continua 65 3 1905 1924 2020Search in Google Scholar

[12]Sharma S., Samanta G.P., Drinking as an epidemic: a mathematical model with dynamic behaviour, Journal of Applied Mathematics and Informatics, 31(1–2), 1–25, 2013. SharmaS. SamantaG.P. Drinking as an epidemic: a mathematical model with dynamic behaviour Journal of Applied Mathematics and Informatics 31 1–2 1 25 2013 Search in Google Scholar

[13]Öztürk Z., Bilgil H., Sorgun S., A new application of fractional glucose-insulin model and numerical solutions, Sigma Journal of Engineering and Natural Sciences, 42(3), 1–11, 2024. ÖztürkZ. BilgilH. SorgunS. A new application of fractional glucose-insulin model and numerical solutions Sigma Journal of Engineering and Natural Sciences 42 3 1 11 2024Search in Google Scholar

[14]Kermack W.O., McKendrick A.G., A contribution to the mathematical theory of epidemics, Proceedings of The Royal Society of London: Series A, Containing Papers of a Mathematical and Physical Character, 115(772), 700–721, 1927. KermackW.O. McKendrickA.G. A contribution to the mathematical theory of epidemics Proceedings of The Royal Society of London: Series A, Containing Papers of a Mathematical and Physical Character 115 772 700 721 1927Search in Google Scholar

[15]Yaro D., Omari-Sasu S.K., Harvim P., Saviour A.W., Obeng B.A., Generalized Euler method for modeling measles with fractional differential equations, International Journal of Innovative Research and Development, 4(4), 358–366, 2015. YaroD. Omari-SasuS.K. HarvimP. SaviourA.W. ObengB.A. Generalized Euler method for modeling measles with fractional differential equations International Journal of Innovative Research and Development 4 4 358 366 2015Search in Google Scholar

[16]Öztürk Z., Bilgil H., Sorgun S., Stability analysis of fractional PSQ_p smoking model and application in Turkey, New Trends in Mathematical Sciences, 10(4), 54–62, 2022. ÖztürkZ. BilgilH. SorgunS. Stability analysis of fractional PSQ_p smoking model and application in Turkey New Trends in Mathematical Sciences 10 4 54 62 2022Search in Google Scholar

[17]Bilgil H., Yousef A., Erciyes A., Erdinç Ü., Öztürk Z., A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event, Journal of Computational and Applied Mathematics, 425, 115015, 2023. BilgilH. YousefA. ErciyesA. ErdinçÜ. ÖztürkZ. A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event Journal of Computational and Applied Mathematics 425 115015 2023 Search in Google Scholar

[18]Tarakçı R., Gözükızıl Ö.F., Examination of stability analysis of Sakarya and Turkey scale alcohol use model, Sakarya University Journal of Science, 25(6), 1332–1342, 2021. TarakçıR. GözükızılÖ.F. Examination of stability analysis of Sakarya and Turkey scale alcohol use model Sakarya University Journal of Science 25 6 1332 1342 2021Search in Google Scholar

[19]Öztürk Z., Bilgil H., Sorgun S., Fractional SIQRV model for COVID-19 and numerical solutions, Konuralp Journal of Mathematics, 11(2), 131–140, 2023. ÖztürkZ. BilgilH. SorgunS. Fractional SIQRV model for COVID-19 and numerical solutions Konuralp Journal of Mathematics 11 2 131 140 2023Search in Google Scholar

[20]Öztürk Z., Bilgil H., Sorgun S., Application of fractional SPR psychological disease model in Turkey and stability analysis, Journal of Mathematical Sciences and Modelling, 6(2), 49–55, 2023. ÖztürkZ. BilgilH. SorgunS. Application of fractional SPR psychological disease model in Turkey and stability analysis Journal of Mathematical Sciences and Modelling 6 2 49 55 2023Search in Google Scholar

[21]Esen A., Ucar Y., Yagmurlu N., Tasbozan O., A Galerkin finite element method to solve fractional diffusion and fractional diffusion-wave equations, Mathematical Modelling and Analysis, 18(2), 260–273, 2013. EsenA. UcarY. YagmurluN. TasbozanO. A Galerkin finite element method to solve fractional diffusion and fractional diffusion-wave equations Mathematical Modelling and Analysis 18 2 260 273 2013Search in Google Scholar

[22]Esen A., Yagmurlu N., Tasbozan O., Approximate analytical solution to time-fractional damped Burger and Cahn-Allen equations, Applied Mathematics and Information Sciences, 7(5), 1951–1956, 2013. EsenA. YagmurluN. TasbozanO. Approximate analytical solution to time-fractional damped Burger and Cahn-Allen equations Applied Mathematics and Information Sciences 7 5 1951 1956 2013Search in Google Scholar

[23]Tasbozan O., Esen A., Yagmurlu N.M., Ucar Y., A numerical solution to fractional diffusion equation for force-free case, Abstract and Applied Analysis, 2013(ID:187383), 1–6, 2013. TasbozanO. EsenA. YagmurluN.M. UcarY. A numerical solution to fractional diffusion equation for force-free case Abstract and Applied Analysis 2013 (ID:187383) 1 6 2013 Search in Google Scholar

[24]Abidemi A., Owolabi K.M., Pindza E., Assessing the dynamics of Lassa fever with impact of environmental sanitation: optimal control and cost-effectiveness analysis, Modeling Earth Systems and Environment, 9(2), 2259–2284, 2023. AbidemiA. OwolabiK.M. PindzaE. Assessing the dynamics of Lassa fever with impact of environmental sanitation: optimal control and cost-effectiveness analysis Modeling Earth Systems and Environment 9 2 2259 2284 2023Search in Google Scholar

[25]Olaniyi S., Alade T.O., Chuma F.M., Ogunsola A.W., Aderele O.R., Abimbade S.F., A fractional-order nonlinear model for a within-host chikungunya virus dynamics with adaptive immunity using Caputo derivative operator, Healthcare Analytics, 4, 100205, 2023. OlaniyiS. AladeT.O. ChumaF.M. OgunsolaA.W. AdereleO.R. AbimbadeS.F. A fractional-order nonlinear model for a within-host chikungunya virus dynamics with adaptive immunity using Caputo derivative operator Healthcare Analytics 4 100205 2023 Search in Google Scholar

[26]Abidemi A., Owolabi K.M., Pindza E., Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission, Physica A: Statistical Mechanics and its Applications, 597, 127259, 2022. AbidemiA. OwolabiK.M. PindzaE. Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission Physica A: Statistical Mechanics and its Applications 597 127259 2022 Search in Google Scholar

[27]Karaagac B., Owolabi K.M., Numerical analysis of polio model: a mathematical approach to epidemiological model using derivative with Mittag–Leffler kernel, Mathematical Methods in the Applied Sciences, 46(7), 8175–8192, 2023. KaraagacB. OwolabiK.M. Numerical analysis of polio model: a mathematical approach to epidemiological model using derivative with Mittag–Leffler kernel Mathematical Methods in the Applied Sciences 46 7 8175 8192 2023Search in Google Scholar

[28]Naik P.A., Owolabi K.M., Zu J., Naik M.U.D., Modeling the transmission dynamics of COVID-19 pandemic in Caputo type fractional derivative, Journal of Multiscale Modelling, 12(03), 2150006, 2021. NaikP.A. OwolabiK.M. ZuJ. NaikM.U.D. Modeling the transmission dynamics of COVID-19 pandemic in Caputo type fractional derivative Journal of Multiscale Modelling 12 03 2150006 2021 Search in Google Scholar

[29]Naik P.A., Owolabi K.M., Yavuz M., Zu J., Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells, Chaos Solitons and Fractals, 140, 110272, 2020. NaikP.A. OwolabiK.M. YavuzM. ZuJ. Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells Chaos Solitons and Fractals 140 110272 2020 Search in Google Scholar

[30]Naik P.A., Zu J., Owolabi K.M., Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control, Chaos Solitons and Fractals, 138, 109826, 2020. NaikP.A. ZuJ. OwolabiK.M. Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control Chaos Solitons and Fractals 138 109826 2020 Search in Google Scholar