SIAM Journal on Applied Mathematics, Volume 81, Issue 1, Page 190-207, January 2021.
The coronavirus disease 2019 (COVID-19) pandemic is changing and impacting lives on a global scale. In this paper, we introduce a mean-field game model in controlling the propagation of epidemics on a spatial domain. The control variable, the spatial velocity, is first introduced for the classical disease models, such as the SIR model. For this proposed model, we provide fast numerical algorithms based on proximal primal-dual methods. Numerical experiments demonstrate that the proposed model illustrates how to separate infected patients in a spatial domain effectively.

中文翻译：

---

通过均场控制来控制流行病的传播

SIAM应用数学杂志，第81卷，第1期，第190-207页，2021
年1月。2019年冠状病毒病（COVID-19）大流行正在改变并影响着全球范围的生命。在本文中，我们引入了均值场博弈模型来控制流行病在空间域上的传播。首先针对经典疾病模型（例如SIR模型）引入控制变量（空间速度）。对于此提出的模型，我们提供了基于近邻原始对偶方法的快速数值算法。数值实验表明，所提出的模型说明了如何有效地在空间范围内分离感染患者。