Mathematical Modelling of Gambling Addiction Dynamics in Society

Hillary Kiprop Kosgei; Phylis Jerotich Kibet

doi:doi:10.11648/j.acm.20251405.15

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Mathematical Modelling of Gambling Addiction Dynamics in Society

Hillary Kiprop Kosgei^*

, Phylis Jerotich Kibet

Published in Applied and Computational Mathematics (Volume 14, Issue 5)

Received: 8 October 2025 Accepted: 18 October 2025 Published: 31 October 2025

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Abstract

Gambling addiction is a silent monster that pose a serious public health threat globally. For instance, compulsive gambling has led to family breakdowns, legal troubles, financial ruins, significant health issues, strained relationships, or even loss of lives. In this study, we formulate and analyze a gambling addiction mathematical model to understand and manage a gambling problem in society. The basic properties of the model were established to show that the model is mathematically and biologically feasible. The basic reproduction number, ℜ₀ was obtained using the next generation matrix method. The conditions for the existence of gambling free equilibrium and gambling endemic equilibrium were established, that is, both equilibria states were found to be locally and globally asymptotically stable whenever ℜ₀ < 1 and unstable when ℜ₀ > 1. Numerical simulation results shows that management of gambling problem depends on the control efforts invested, for instance, higher control efforts increase the chances of overcoming the challenge. The model results further reveal that the rate of contact between susceptible individuals and gamblers (casual and heavy) influences the development of gambling habits in the community. The study findings also show that serious early gambling interventions play a predominant role in mitigating this harmful behavior in society.

Published in	Applied and Computational Mathematics (Volume 14, Issue 5)
DOI	10.11648/j.acm.20251405.15
Page(s)	293-300
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Mathematical Model, Gambling Addiction, Gambling Control, Gambling Problem, Gambling Interventions

References

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[2]	Bitanihirwe, B. K. Y., Adebisi, T., Bunn, C., Ssewanyana, D., Darby, P., & Kitchin, P. (2022). Gambling in Sub-Saharan Africa: Traditional Forms and Emerging Technologies. Current addiction reports, 9(4), 373–384. https://doi.org/10.1007/s40429-022-00449-0
[3]	Chóliz, M., Marcos, M., & Lázaro-Mateo, J. (2021). The risk of online gambling: A study of gambling disorder prevalence rates in Spain. International Journal of Mental Health and Addiction, 19(2), 404–417. https://doi.org/10.1007/s11469-019-00067-4
[4]	Dellosa, G., & Browne, M. (2024). The influence of age on gambling problems worldwide: A systematic review and meta-analysis of risk among younger, middle-aged, and older adults. Journal of behavioral addictions, 13(3), 702–715. https://doi.org/10.1556/2006.2024.00051
[5]	Hayano, S., Dong, R., Miyata, Y., & Kasuga, S. (2021). The study of differences by region and type of gambling on the degree of gambling addiction in Japan. Scientific reports, 11(1), 13102. https://doi.org/10.1038/s41598-021-92137-8
[6]	Hillary Kiprop Kosgei. (2022). Modelling HIV/AIDS Infection Dynamics in the Presence of Interfered Interventions. Journal of Advances in Mathematics and Computer Science, 37(4), 31-52. https://doi.org/ 10.9734/jamcs/2022/v37i430447
[7]	Lugina, N. A., & Kytun, A. P. (2019). A Person with a Game Addiction as a Victim of the Crime of Gambling. JE Eur. L., 136. https://doi.org/10.5281/zenodo.3608058
[8]	Maina, M. M. (2020). Factors influencing growth of gambling activities in Kenya (Doctoral dissertation, Strathmore University). http://hdl.handle.net/11071/10425
[9]	Miriti, A. G. (2020). Prevalence of gambling disorder among patients seeking psychiatric treatment at Mathari national teaching and referral hospital in Nairobi, Kenya (Doctoral dissertation, University of Nairobi). http://erepository.uonbi.ac.ke/handle/11295/154031
[10]	Noel, J. K., et al. (2024). Internet, app-based, and casino gambling: Associations with problem gambling symptoms among U.S. young adults. https://doi.org/10.1007/s10899-024-10284-9
[11]	Romeu, R. J., Haines, N., Ahn, W. Y., Busemeyer, J. R., & Vassileva, J. (2020). A computational model of the Cambridge gambling task with applications to substance use disorders. Drug and alcohol dependence, 206, 107711. https://doi.org/10.1016/j.drugalcdep.2019.107711
[12]	Serna, C., García-Perales, J., & Martínez, I. (2023). Protective and risk parenting styles for internet and online gambling addiction. Human Behavior and Emerging Technologies, 2023(1), 6674541. https://doi.org/10.1155/2023/6674541
[13]	Ssewanyana, D., & Bitanihirwe, B. (2018). Problem Gambling among Young People in Sub-Saharan Africa. Frontiers in public health, 6, 23. https://doi.org/10.3389/fpubh.2018.00023
[14]	Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 180, 29–48. https://doi.org/10.1016/s0025-5564(02)00108-6
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APA Style

Kosgei, H. K., Kibet, P. J. (2025). Mathematical Modelling of Gambling Addiction Dynamics in Society. Applied and Computational Mathematics, 14(5), 293-300. https://doi.org/10.11648/j.acm.20251405.15

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ACS Style

Kosgei, H. K.; Kibet, P. J. Mathematical Modelling of Gambling Addiction Dynamics in Society. Appl. Comput. Math. 2025, 14(5), 293-300. doi: 10.11648/j.acm.20251405.15

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AMA Style

Kosgei HK, Kibet PJ. Mathematical Modelling of Gambling Addiction Dynamics in Society. Appl Comput Math. 2025;14(5):293-300. doi: 10.11648/j.acm.20251405.15

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@article{10.11648/j.acm.20251405.15,
  author = {Hillary Kiprop Kosgei and Phylis Jerotich Kibet},
  title = {Mathematical Modelling of Gambling Addiction Dynamics in Society
},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {5},
  pages = {293-300},
  doi = {10.11648/j.acm.20251405.15},
  url = {https://doi.org/10.11648/j.acm.20251405.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251405.15},
  abstract = {Gambling addiction is a silent monster that pose a serious public health threat globally. For instance, compulsive gambling has led to family breakdowns, legal troubles, financial ruins, significant health issues, strained relationships, or even loss of lives. In this study, we formulate and analyze a gambling addiction mathematical model to understand and manage a gambling problem in society. The basic properties of the model were established to show that the model is mathematically and biologically feasible. The basic reproduction number, ℜ0 was obtained using the next generation matrix method. The conditions for the existence of gambling free equilibrium and gambling endemic equilibrium were established, that is, both equilibria states were found to be locally and globally asymptotically stable whenever ℜ0 0 > 1. Numerical simulation results shows that management of gambling problem depends on the control efforts invested, for instance, higher control efforts increase the chances of overcoming the challenge. The model results further reveal that the rate of contact between susceptible individuals and gamblers (casual and heavy) influences the development of gambling habits in the community. The study findings also show that serious early gambling interventions play a predominant role in mitigating this harmful behavior in society. 
},
 year = {2025}
}

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TY  - JOUR
T1  - Mathematical Modelling of Gambling Addiction Dynamics in Society

AU  - Hillary Kiprop Kosgei
AU  - Phylis Jerotich Kibet
Y1  - 2025/10/31
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251405.15
DO  - 10.11648/j.acm.20251405.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 293
EP  - 300
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20251405.15
AB  - Gambling addiction is a silent monster that pose a serious public health threat globally. For instance, compulsive gambling has led to family breakdowns, legal troubles, financial ruins, significant health issues, strained relationships, or even loss of lives. In this study, we formulate and analyze a gambling addiction mathematical model to understand and manage a gambling problem in society. The basic properties of the model were established to show that the model is mathematically and biologically feasible. The basic reproduction number, ℜ0 was obtained using the next generation matrix method. The conditions for the existence of gambling free equilibrium and gambling endemic equilibrium were established, that is, both equilibria states were found to be locally and globally asymptotically stable whenever ℜ0 0 > 1. Numerical simulation results shows that management of gambling problem depends on the control efforts invested, for instance, higher control efforts increase the chances of overcoming the challenge. The model results further reveal that the rate of contact between susceptible individuals and gamblers (casual and heavy) influences the development of gambling habits in the community. The study findings also show that serious early gambling interventions play a predominant role in mitigating this harmful behavior in society. 

VL  - 14
IS  - 5
ER  -

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Author Information

Hillary Kiprop Kosgei

Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya

Contact Email

http://orcid.org/0009-0005-2046-152X
Phylis Jerotich Kibet

Department of Public Health, Kabarak University, Nakuru, Kenya

Contact Email

http://orcid.org/0000-0002-5699-8266

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APA Style

Kosgei, H. K., Kibet, P. J. (2025). Mathematical Modelling of Gambling Addiction Dynamics in Society. Applied and Computational Mathematics, 14(5), 293-300. https://doi.org/10.11648/j.acm.20251405.15

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ACS Style

Kosgei, H. K.; Kibet, P. J. Mathematical Modelling of Gambling Addiction Dynamics in Society. Appl. Comput. Math. 2025, 14(5), 293-300. doi: 10.11648/j.acm.20251405.15

Copy | Download

AMA Style

Kosgei HK, Kibet PJ. Mathematical Modelling of Gambling Addiction Dynamics in Society. Appl Comput Math. 2025;14(5):293-300. doi: 10.11648/j.acm.20251405.15

Copy | Download

@article{10.11648/j.acm.20251405.15,
  author = {Hillary Kiprop Kosgei and Phylis Jerotich Kibet},
  title = {Mathematical Modelling of Gambling Addiction Dynamics in Society
},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {5},
  pages = {293-300},
  doi = {10.11648/j.acm.20251405.15},
  url = {https://doi.org/10.11648/j.acm.20251405.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251405.15},
  abstract = {Gambling addiction is a silent monster that pose a serious public health threat globally. For instance, compulsive gambling has led to family breakdowns, legal troubles, financial ruins, significant health issues, strained relationships, or even loss of lives. In this study, we formulate and analyze a gambling addiction mathematical model to understand and manage a gambling problem in society. The basic properties of the model were established to show that the model is mathematically and biologically feasible. The basic reproduction number, ℜ0 was obtained using the next generation matrix method. The conditions for the existence of gambling free equilibrium and gambling endemic equilibrium were established, that is, both equilibria states were found to be locally and globally asymptotically stable whenever ℜ0 0 > 1. Numerical simulation results shows that management of gambling problem depends on the control efforts invested, for instance, higher control efforts increase the chances of overcoming the challenge. The model results further reveal that the rate of contact between susceptible individuals and gamblers (casual and heavy) influences the development of gambling habits in the community. The study findings also show that serious early gambling interventions play a predominant role in mitigating this harmful behavior in society. 
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Modelling of Gambling Addiction Dynamics in Society

AU  - Hillary Kiprop Kosgei
AU  - Phylis Jerotich Kibet
Y1  - 2025/10/31
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251405.15
DO  - 10.11648/j.acm.20251405.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 293
EP  - 300
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20251405.15
AB  - Gambling addiction is a silent monster that pose a serious public health threat globally. For instance, compulsive gambling has led to family breakdowns, legal troubles, financial ruins, significant health issues, strained relationships, or even loss of lives. In this study, we formulate and analyze a gambling addiction mathematical model to understand and manage a gambling problem in society. The basic properties of the model were established to show that the model is mathematically and biologically feasible. The basic reproduction number, ℜ0 was obtained using the next generation matrix method. The conditions for the existence of gambling free equilibrium and gambling endemic equilibrium were established, that is, both equilibria states were found to be locally and globally asymptotically stable whenever ℜ0 0 > 1. Numerical simulation results shows that management of gambling problem depends on the control efforts invested, for instance, higher control efforts increase the chances of overcoming the challenge. The model results further reveal that the rate of contact between susceptible individuals and gamblers (casual and heavy) influences the development of gambling habits in the community. The study findings also show that serious early gambling interventions play a predominant role in mitigating this harmful behavior in society. 

VL  - 14
IS  - 5
ER  -

Copy | Download