Yes. This has been possible since the 1990's. In the US recently, the flu vaccine was recently offered as a nasal spray.
There is current research being done to aerosolize several vaccines. Public health officials have an interest in this method due to it being less expensive to produce, more people can receive the vaccine in a shorter time frame, and less need for infrastructure.
In India, they have started to give children aerosolized versions of the Measles vaccine. From research published in 2015 in The New England Journal of Medicine, scientists were reviewing how effective the aerosolized version is against the vaccine given subcutaneously. Even though the group's statistically analysis of the children's seropositivity, a method derived from previous studies, demonstrated the aerosol vaccine was statistically "inferior" to vaccines given sub-q. However, both groups of children had the same protection from the Measles.
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