  With the invention of the COVID-19 vaccine, shipping and distributing are
crucial in controlling the pandemic. In this paper, we build a mean-field
variational problem in a spatial domain, which controls the propagation of
pandemic by the optimal transportation strategy of vaccine distribution. Here
we integrate the vaccine distribution into the mean-field SIR model designed in
our previous paper arXiv:2006.01249. Numerical examples demonstrate that the
proposed model provides practical strategies in vaccine distribution on a
spatial domain.
