Dr. Suzanne Humphries, M.D. – Vaccine Strain of Measles Virus Found in Measles Outbreaks
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Dr. Suzanne Humphries is a practicing nephrologist (kidney physician). In this lecture (video below), she addresses a study done in Croatia  where a child who was vaccinated with the MMR vaccine was tested positive for the measles vaccine strain Schwarz eight days after vaccination.
This was a significant finding, because the child’s symptoms were thought to be similar to rubella, and without testing, the sickness would have been possibly mis-diagnosed as rubella, or the wild-type strain of measles the vaccine is designed to protect against.
This concept of “shedding,” where the child comes down with the disease from the virus in the vaccine itself, surprised the researchers:
Virus excretion in vaccinees has been reported before, but to our knowledge, this is documented for the first time for the Schwarz vaccine strain. 
Since 2010, this phenomena of vaccine shedding with measles in the MMR vaccine has been observed in at least two other studies:
Differentiating the wild from the attenuated during a measles outbreak. Paediatrcis and Child Health, 2012:
In the midst of a local measles outbreak, a recently immunized child was investigated for a new-onset measles-type rash. Nucleic acid testing identified that a vaccine-type measles virus was being shed in the urine. Clinically differentiating measles from a nonmeasles rash is challenging, but can be supported by a thorough medical history evaluation. Rashes are expected to occur after immunization; nucleic acid testing can be used when it is difficult to differentiate between wild and attenuated strains. 
Case of vaccine-associated measles five weeks post-immunisation, British Columbia, Canada, Eurosurveillance, 2013:
We describe a case of vaccine-associated measles in a two-year-old patient from British Columbia, Canada, in October 2013, who received her first dose of measles-containing vaccine 37 days prior to onset of prodromal symptoms. Identification of this delayed vaccine-associated case occurred in the context of an outbreak investigation of a measles cluster.