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.

翻译：流行病（如新型冠状病毒）的建模与控制已具有全球性的重要意义。在此背景下，一个自然而有力的动态建模框架是连续时间马尔可夫决策过程，该模型包含了经典的舱室模型范式，如易感-感染-康复模型。基于CTMDP的模型所面临的挑战促使我们寻求更高效的方法，而平均场方法则提供了一种有效的替代方案。平均场方法通过计算由大量交互节点（节点代表群体中的个体）组成的动态系统的集体行为来进行建模。本文（a）概述了基于平均场方法的流行病建模与控制，并（b）提供了该主题最新进展的最新更新。本文的讨论沿着两条具体线索展开。第一条线索假设个体节点忠实地遵循监管机构制定的社会最优控制策略。第二条线索允许个体节点表现出独立的、策略性的行为。在这种情况下，策略性互动被建模为平均场博弈，控制则基于相关的平均场纳什均衡。本文首先讨论了使用扩展舱室模型（SIVR）对流行病进行建模，并给出了一个示例。接着，我们回顾了基于平均场方法的相关文献，内容涉及流行病的最优控制，即探讨监管机构如何最优地遏制流行病在人群中的传播。随后，我们更新了关于基于平均场博弈的方法在流行病传播与控制研究中应用的文献综述。最后，本文指出了相关的未来研究方向。