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

arXiv: https://arxiv.org/abs/2012.06745 · HTML: https://mlsanity.com/paper/2012.06745/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2020.

## Built on by (most cited first, 6 of 6)

- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence](https://mlsanity.com/paper/2204.11924/) (2022)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [A Class of Dimension-free Metrics for the Convergence of Empirical Measures](https://mlsanity.com/paper/2104.12036/) (2021)
- [Recurrent Neural Networks for Stochastic Control Problems with Delay](https://mlsanity.com/paper/2101.01385/) (2021)
- [Pandemic Control, Game Theory and Machine Learning](https://mlsanity.com/paper/2208.08646/) (2022)

## Abstract (arXiv)

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.