  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.
