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

Yao Xuan, Robert Balkin, Jiequn Han, Ruimeng Hu, Hector D Ceniceros
Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, PMLR 145:987-1012, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v145-xuan22a, title = {Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm}, author = {Xuan, Yao and Balkin, Robert and Han, Jiequn and Hu, Ruimeng and Ceniceros, Hector D}, booktitle = {Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference}, pages = {987--1012}, year = {2022}, editor = {Bruna, Joan and Hesthaven, Jan and Zdeborova, Lenka}, volume = {145}, series = {Proceedings of Machine Learning Research}, month = {16--19 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v145/xuan22a/xuan22a.pdf}, url = {https://proceedings.mlr.press/v145/xuan22a.html}, 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. } }
Endnote
%0 Conference Paper %T Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm %A Yao Xuan %A Robert Balkin %A Jiequn Han %A Ruimeng Hu %A Hector D Ceniceros %B Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference %C Proceedings of Machine Learning Research %D 2022 %E Joan Bruna %E Jan Hesthaven %E Lenka Zdeborova %F pmlr-v145-xuan22a %I PMLR %P 987--1012 %U https://proceedings.mlr.press/v145/xuan22a.html %V 145 %X 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.
APA
Xuan, Y., Balkin, R., Han, J., Hu, R. & Ceniceros, H.D.. (2022). Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm. Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, in Proceedings of Machine Learning Research 145:987-1012 Available from https://proceedings.mlr.press/v145/xuan22a.html.

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