The recent outbreak of measles in Disneyland California was the result of poor vaccination rates, scientists have said, with as few as 50% of people protected against the disease.

Researchers at Boston Children's Hospital found that vaccine coverage among exposed populations is far below what is needed to keep the virus at bay.

Findings, published online by JAMA Paediatrics, showed that vaccinate rates were between 50 and 86%. For sufficient herd immunity, rates need to be between 96 and 99%.

The Disneyland measles outbreak has seen over 130 people infected by the disease. The outbreak started in December, and state officials say it is now subsiding, with only three cases reported since the end of February.

The outbreak served to highlight the number of people who have not been vaccinated against measles – with huge amounts of misinformation online spurring parents to 'say no' to protecting their children from measles, mumps and rubella.

Researchers examined data from the California Department of Public Health as well as case data from the HealthMap disease surveillance system.

Findings showed vaccine coverage among exposed populations – in California, Arizona and Illinois – is far below what is required to safeguard populations. It is also the first study to link vaccination rates to the measles outbreak.

Measles is very contagious – for every person infected, it will spread to between 11 and 18 among populations susceptible to the disease (the virus's R0, or basic reproduction rate). In populations where some individuals are immune (through vaccination) the virus spreads more slowly.

Authors calculated the virus effective reproduction rate to work out the vaccinate rates – they were not based on information on percentages of the population that have or have not been vaccinated.

"It's as though you took everyone exposed to measles in the areas with case clusters, put them in a room and measured the level of vaccine coverage in that aggregate population," lead author Maimuna Majumder explained.

John Brownstein, who also led the research, added: "Our data tell us a very straightforward story – that the way to stop this and future measles outbreaks is through vaccination. The fundamental reason why we're seeing the number of cases we are is inadequate vaccine coverage among the exposed."