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Recent advances in modeling and control of epidemics using a mean field approach

Roy, A and Singh, C and Narahari, Y (2023) Recent advances in modeling and control of epidemics using a mean field approach. In: Sadhana - Academy Proceedings in Engineering Sciences, 48 (4).

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Official URL: https://doi.org/10.1007/s12046-023-02268-z


The modeling and control of epidemics, such as the novel Coronavirus, have become crucial on a global scale, for effective management of epidemic situations. This paper is focused on using the mean field approach for modeling and control of epidemics. The mean field approach is an effective alternative to the classical approach of using continuous time Markov decision process (CTMDP) models, which suffer from the curse of dimensionality and entail knowledge of global state information. The mean field approach captures the collective behavior of a dynamic system consisting of numerous interacting nodes representing individuals in the population. The objectives of this paper are twofold: (a) to provide an overview of the mean field approach to epidemic modeling and control, and (b) to present recent advances in this area. Emphasizing the importance of containing and suppressing epidemic spread through non-pharmaceutical interventions, the paper highlights the need to minimize loss of lives, reduce suffering, and alleviate the burden on the public healthcare system. A potential challenge here is the presence of a section of the population who act on their free will and deviate from recommended best practices, which could lead to a potential public health crisis. Motivated by this, the paper explores two specific threads to modeling and control. The first thread assumes that individual nodes comply with a socially optimal control policy mandated by a regulatory authority. The second thread allows for independent and strategic behavior by the individual nodes, modeled as a mean field game, where the strategies of rational agents are based on mean field Nash equilibria. The paper begins by discussing the modeling of epidemics using an extended SIVR (Susceptible-Infected-Vaccinated-Recovered) compartmental model, accompanied by an illustrative example. Next, a literature review is provided, focusing on the mean field approach for socially optimal control of epidemics and how a regulatory authority can effectively contain the spread. Subsequently, the paper presents an update on the use of mean field game-based approaches in studying epidemic spread and control. Finally, future research directions in this important area are discussed. © 2023, Indian Academy of Sciences.

Item Type: Journal Article
Publication: Sadhana - Academy Proceedings in Engineering Sciences
Publisher: Springer
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Continuous time systems; Coronavirus; Disease control, Epidemic game; Field-control; Mean field control; Mean field nash equilibrium; Mean-field; Mean-field games; Nash equilibria; Optimal controls; Population games; Stackelberg Games, Markov processes
Department/Centre: Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 05 Dec 2023 09:33
Last Modified: 05 Dec 2023 09:33
URI: https://eprints.iisc.ac.in/id/eprint/83361

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