Mean field control problems for vaccine distribution

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 pandemics by the optimal transportation strategy of vaccine distribution. Here, we integrate the vaccine distribution into the mean-field SIR model designed in Lee W, Liu S, Tembine H, Li W, Osher S (2020) Controlling propagation of epidemics via mean-field games. arXiv preprint arXiv:2006.01249. Numerical examples demonstrate that the proposed model provides practical strategies for vaccine distribution in a spatial domain.