  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.
