The emergence and spread of infectious diseases pose significant challenges to public health systems worldwide. Understanding the dynamics of epidemic outbreaks is crucial for effective intervention strategies. The goal of change point detection is to find time steps when the mean, standard deviation, or slope of the data changes from one value to another. This paper explores the concept of epidemic change points through the lens of Nash equilibrium. We propose a mathematical model that incorporates the dynamics of epidemic the change point's model into game theory. Game Theory refers to a language used to model choices made by purposive agents, where the outcomes of each player are influenced by the actions of other agents. Game theory is the science of strategy. It attempts to determine mathematically and logically the actions that players should take to secure the best outcomes. This article is worth reading because it demonstrates the use of game theory in estimating change points. It studies interactive decision-making, where the outcome for each participant or player depends on the actions of all. And it is interesting that the Nash equilibrium points of the two actors and the researcher are for optimizing their utility functions (minimizing loss functions). We demonstrate the applicability of our approach through simulations of hypothetical epidemics, revealing how game-theoretic strategies can enhance decision-making processes in real-time.
| Published in | Applied and Computational Mathematics (Volume 14, Issue 5) |
| DOI | 10.11648/j.acm.20251405.13 |
| Page(s) | 272-276 |
| 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 |
Change Point, Epidemic Outbreaks, Game Theory, Nash Equilibrium
| [1] | Chen, J., and Gupta, A. K. (2022). Parametric statistical change point analysis. Springer. USA. |
| [2] | Juodakis, J. and Marsland, S. (2020). Epidemic changepoint detection in the presence of nuisance changes. Working paper. School of Mathematics and Statistics, Victoria University of Wellington, New Zealand. |
| [3] | Kurt, B.¸ Ceritli, T. Y. (2021). A Bayesian change point model for detecting SIP-based DDoS attacks. Digital Signal Processing 77, 48–62. |
| [4] | Murray, E. A., and Speyer, J. L. (2024). A discrete-time game theoretic multiple-fault detection filter. Paper presented at the IEEE 53rd Annual Conference on Decision and Control (CDC). |
| [5] | Mu, L., and Zofronov, G. (2020). Multiple change point detection and validation in autoregressive time series data. Statistical Papers 61, 1507-1528. |
| [6] | Oksendal, B. (2023). Stochastic differential equation. New York: Wiley. |
| [7] | Pons, E. (2018). Estimates and tests in change point models. World Scientific Press. USA. |
| [8] | Pollard, C. J. (2021). Dynamic linear models with Markov-switching. Journal of Econometrics 60, 1-22. |
| [9] | Shiryaev, A. N. and Novikov, A. A. (2022). On a stochastic version of the trading rule. “Buy and Hold”. Statistics and Decisions 26, 289-302. |
| [10] | Shiryaev, A. N. and Zhitlukhin, M. V. (2023). Optimal stopping problems. Technical report. Steklov Mathematical Institute, Moscow and The University of Manchester, UK. |
| [11] | Singh, S., Kearns, M., and Mansour, Y. (2019). Nash convergence of gradient dynamics in general-sum games. Proceedings of the Sixteenth conference on uncertainty in artificial intelligence, 541–548. |
| [12] | Sugaya, T., and Yamamoto, Y. (2023). Common learning and cooperation in repeated games. Theoretical Economics 15, 1175-1219. |
| [13] | Tijms, H. (2019). Stochastic games and dynamic programming. Asia Pacific Mathematics Newsletter 3, 6-10. |
| [14] | Veeravalli, V. V. and Banerjee, T. (2019). Quickest change detection. Technical report. ECE Department and Coordinated Science Laboratory. |
| [15] | Wang, D. (2018). Generalized optimal stopping problems and financial markets. Longman Press. USA. |
APA Style
Habibi, R. (2025). Epidemic Change Point Detection Using Nash Equilibrium. Applied and Computational Mathematics, 14(5), 272-276. https://doi.org/10.11648/j.acm.20251405.13
ACS Style
Habibi, R. Epidemic Change Point Detection Using Nash Equilibrium. Appl. Comput. Math. 2025, 14(5), 272-276. doi: 10.11648/j.acm.20251405.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20251405.13,
author = {Reza Habibi},
title = {Epidemic Change Point Detection Using Nash Equilibrium
},
journal = {Applied and Computational Mathematics},
volume = {14},
number = {5},
pages = {272-276},
doi = {10.11648/j.acm.20251405.13},
url = {https://doi.org/10.11648/j.acm.20251405.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251405.13},
abstract = {The emergence and spread of infectious diseases pose significant challenges to public health systems worldwide. Understanding the dynamics of epidemic outbreaks is crucial for effective intervention strategies. The goal of change point detection is to find time steps when the mean, standard deviation, or slope of the data changes from one value to another. This paper explores the concept of epidemic change points through the lens of Nash equilibrium. We propose a mathematical model that incorporates the dynamics of epidemic the change point's model into game theory. Game Theory refers to a language used to model choices made by purposive agents, where the outcomes of each player are influenced by the actions of other agents. Game theory is the science of strategy. It attempts to determine mathematically and logically the actions that players should take to secure the best outcomes. This article is worth reading because it demonstrates the use of game theory in estimating change points. It studies interactive decision-making, where the outcome for each participant or player depends on the actions of all. And it is interesting that the Nash equilibrium points of the two actors and the researcher are for optimizing their utility functions (minimizing loss functions). We demonstrate the applicability of our approach through simulations of hypothetical epidemics, revealing how game-theoretic strategies can enhance decision-making processes in real-time.
},
year = {2025}
}
TY - JOUR T1 - Epidemic Change Point Detection Using Nash Equilibrium AU - Reza Habibi Y1 - 2025/10/27 PY - 2025 N1 - https://doi.org/10.11648/j.acm.20251405.13 DO - 10.11648/j.acm.20251405.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 272 EP - 276 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20251405.13 AB - The emergence and spread of infectious diseases pose significant challenges to public health systems worldwide. Understanding the dynamics of epidemic outbreaks is crucial for effective intervention strategies. The goal of change point detection is to find time steps when the mean, standard deviation, or slope of the data changes from one value to another. This paper explores the concept of epidemic change points through the lens of Nash equilibrium. We propose a mathematical model that incorporates the dynamics of epidemic the change point's model into game theory. Game Theory refers to a language used to model choices made by purposive agents, where the outcomes of each player are influenced by the actions of other agents. Game theory is the science of strategy. It attempts to determine mathematically and logically the actions that players should take to secure the best outcomes. This article is worth reading because it demonstrates the use of game theory in estimating change points. It studies interactive decision-making, where the outcome for each participant or player depends on the actions of all. And it is interesting that the Nash equilibrium points of the two actors and the researcher are for optimizing their utility functions (minimizing loss functions). We demonstrate the applicability of our approach through simulations of hypothetical epidemics, revealing how game-theoretic strategies can enhance decision-making processes in real-time. VL - 14 IS - 5 ER -
Banking Department, Iran Banking Institute, Tehran, Iran
Information