Controlling Propagation of epidemics via mean-field control

TL;DR

This paper introduces a mean-field game model with spatial control for epidemic propagation, providing efficient algorithms and demonstrating effective separation of infected individuals spatially.

Contribution

It develops a novel mean-field control framework with spatial velocity control for epidemic models like SIR, along with fast numerical algorithms.

Findings

Effective separation of infected individuals demonstrated

Fast proximal primal-dual algorithms developed

Model provides spatial control insights for epidemic management

Abstract

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.