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There have been two confirmed cases of measles in the Towns.
Parents have been advised to vaccinate their children after the outbreak in Cuxton.
Letters were sent to schools, nurseries and health providers in the area to warn people.
Public Health England wants to advise parents and carers on the best course of action to contain the illness.
Consultant in communicable disease control for the South East, Dr Claire Winslade said: “Measles is not a harmless childhood illness as many think – it is extremely infectious, can strike anyone and sadly in some instances can have very serious long term and life changing consequences.
“The best form of protection against measles is the MMR vaccination.
"It is important that anyone who hasn’t already had two doses of the MMR vaccine contacts their GP surgery for an appointment to get vaccinated.
“Also remain alert to the symptoms of measles, which can include cold-like symptoms, sore red eyes, a high temperature and a red-brown blotchy rash.
"If you experience these symptoms seek medical attention but be sure to phone ahead before you visit your GP surgery or other healthcare setting, so arrangements can be made to prevent others from being infected.”
How to check your child for measles
Symptoms of measles develop around 10 days after a person is infected. These can include:
Symptoms usually resolve in about 7 to 10 days.
For further information about measles, click here.
Information about the MMR vaccine click here.