Recent Advances in Modeling and Control of Epidemics using a Mean Field Approach

TL;DR

This paper reviews recent advances in epidemic modeling and control using mean field approaches, including social optimal control and game-theoretic strategies, highlighting their effectiveness in managing disease spread.

Contribution

It provides a comprehensive overview of mean field methods in epidemic control, comparing social optimal policies and strategic individual behaviors through game-theoretic models.

Findings

Mean field models effectively capture epidemic dynamics with many interacting individuals.

Strategic behavior modeling via mean field games offers insights into individual decision impacts.

Review of recent literature highlights progress and future directions in epidemic control strategies.

Abstract

Modeling and control of epidemics such as the novel Corona virus have assumed paramount importance at a global level. A natural and powerful dynamical modeling framework to use in this context is a continuous time Markov decision process (CTMDP) that encompasses classical compartmental paradigms such as the Susceptible-Infected-Recovered (SIR) model. The challenges with CTMDP based models motivate the need for a more efficient approach and the mean field approach offers an effective alternative. The mean field approach computes the collective behavior of a dynamical system comprising numerous interacting nodes (where nodes represent individuals in the population). This paper (a) presents an overview of the mean field approach to epidemic modeling and control and (b) provides a state-of-the-art update on recent advances on this topic. Our discussion in this paper proceeds along two specific threads. The first thread assumes that the individual nodes faithfully follow a socially optimal control policy prescribed by a regulatory authority. The second thread allows the individual nodes to exhibit independent, strategic behavior. In this case, the strategic interaction is modeled as a mean field game and the control is based on the associated mean field Nash equilibria. In this paper, we start with a discussion of modeling of epidemics using an extended compartmental model - SIVR and provide an illustrative example. We next provide a review of relevant literature, using a mean field approach, on optimal control of epidemics, dealing with how a regulatory authority may optimally contain epidemic spread in a population. Following this, we provide an update on the literature on the use of the mean field game based approach in the study of epidemic spread and control. We conclude the paper with relevant future research directions.