Davenport served as Vice-President of the Royal Pharmaceutical Society of Great Britain (formerly the Pharmaceutical Society of Great Britain) from 1853–55 and as its President, 1855-56.
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The WHO, the American Academy of Pediatrics, the Advisory Committee on Immunization Practices of the Centers for Disease Control and Prevention, the American Academy of Family Physicians, the British Medical Association and the Royal Pharmaceutical Society of Great Britain currently recommend routine vaccination of children against mumps.