# A Game Theoretic Approach to Control Coronavirus Pandemic

Document Type : Original Paper

Authors

Data Science and Modeling Laboratory, School of Mathematics, Statistics and Computer Science, College of Science, University of Teran, Tehran, Iran

Abstract

Public health and most economic activities have been affected by the coronavirus pandemic. This has caused a lot of difficulties for the public and the governance. A suitable solution that balances public health and economic activities is essential. In this paper, we provide a game-theoretic approach to find this balance, given a desired priority ratio between the two. We propose a Stackelberg game where Corona National Headquarters is the leader, and the people are the followers. We find an optimal solution to the proposed game for different color zones based on the number of patients in a given region. We also find the mixed Nash equilibria of the proposed game and explain the effects of different model parameters on the equilibria. We introduce the optimal mix strategies for each player to control the outbreak. We illustrate the performance of the proposed model for different color zones at different stages of the total deaths curve of the outbreak. Finally, we incorporate the possibility of having inaccurate decisions in the model for real world applications. The proposed strategy could also be used to control other possible respiratory pandemics that spread through close human contacts.

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Main Subjects

#### References

[1] A. Adams, W. Li and C. Zhang, The disguised pandemic: the importance of data normalization in COVID-19 web mapping, Public Health, 183 (2020), 36-37.
[2] B. An, E. Shieh, R. Yang, M. Tambe, C. Baldwin, J. DiRenzo, B. Maule, G. Meyer, PROTECT —A Deployed Game-Theoretic System for Strategic Security Allocation for the United States Coast Guard, AI MAGAZINE, 2012, 96-110.
[3] M. Breton, A. Alj and A. Haurie, Sequential Stackelberg equilibria in two-person games, Journal of Optimization Theory and Applications, 59 (1988), 71-97.
[4] M. J. Osborne, An Introduction to Game Theory, Oxford University Press, 2011, 99-152.
[5] R. W. Saaty, The Analytic Hierarchy Process-What it is and How it is used, Mathl Modeling, 9 (1987), 161-176.
[6] A. Zeb, E. Alzahrani, V. S. Erturk and G. Zaman, Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class, BioMed Research International, 2020, 23-33.
[7] Worldometer real time world statistics, Coronavirus Updates, Retrieved on 23rd February 2023, https://www.worldometers.info/.
[8] اتاق اصناف ایران، فهرست مشاغل و رسته های صنفی براساس گروه های شغلی محدودیت های کرونایی، به دست آمده در تاریخ ۴ اسفند 1401، https://otaghasnafeiran.ir
[9] ، ٩] خبرگزاری جمهوری اسلامی ایران، رنگ بندی کرونایی شهرستان های کشور، به دست آمده در تاریخ ۴ اسفند ١۴٠١، https://www.irna.ir

### History

• Receive Date: 30 May 2022
• Revise Date: 27 February 2023
• Accept Date: 17 May 2023