Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm

TL;DR

This paper develops a multi-region stochastic game model for infectious disease control, applying deep learning algorithms to optimize policies and analyze COVID-19 spread across multiple states.

Contribution

It introduces a realistic multi-region SEIR model with an advanced deep learning algorithm to solve high-dimensional stochastic differential games for pandemic policy optimization.

Findings

Demonstrates the impact of lockdown policies on COVID-19 spread in three states.

Shows how regional policies influence each other’s epidemic outcomes.

Provides a computational framework for real-world pandemic policy analysis.

Abstract

Game theory has been an effective tool in the control of disease spread and in suggesting optimal policies at both individual and area levels. In this paper, we propose a multi-region SEIR model based on stochastic differential game theory, aiming to formulate optimal regional policies for infectious diseases. Specifically, we enhance the standard epidemic SEIR model by taking into account the social and health policies issued by multiple region planners. This enhancement makes the model more realistic and powerful. However, it also introduces a formidable computational challenge due to the high dimensionality of the solution space brought by the presence of multiple regions. This significant numerical difficulty of the model structure motivates us to generalize the deep fictitious algorithm introduced in [Han and Hu, MSML2020, pp.221--245, PMLR, 2020] and develop an improved algorithm to overcome the curse of dimensionality. We apply the proposed model and algorithm to study the COVID-19 pandemic in three states: New York, New Jersey, and Pennsylvania. The model parameters are estimated from real data posted by the Centers for Disease Control and Prevention (CDC). We are able to show the effects of the lockdown/travel ban policy on the spread of COVID-19 for each state and how their policies affect each other.