Weller was born and grew up inAnn Arbor,Michigan, where he graduated fromAnn Arbor High School. He then went to theUniversity of Michigan, where his fatherCarl Vernon Weller was a professor in the Department of Pathology. At Michigan, he studied medical zoology and received a B.S. and an M.S., with his masters thesis on fish parasites.
In 1936, Weller enteredHarvard Medical School, and in 1939 began working under John Franklin Enders, with whom he would later (along with Frederick Chapman Robbins) share the Nobel Prize. It was Enders who got Weller involved in researching viruses and tissue-culture techniques for determining infectious disease causes. Weller received his MD in 1940, and went to work at Children's Hospital inBoston.
In 1942, during World War II, he entered the Army Medical Corps and was stationed at theAntilles Medical Laboratory inPuerto Rico, earning the rank of Major and heading the facility's Departments of Bacteriology, Virology and Parasitology. After the War, he returned to Children's Hospital in Boston, and it was there in 1947, that he rejoined Enders in the newly created Research Division of Infectious Diseases. After several leading positions, in July 1954, he was appointed head of the Tropical Public Health Department at theHarvard School of Public Health. Weller also served from 1953 to 1959 as director of the Commission on Parasitic Diseases of the AmericanArmed Forces Epidemiological Board.
In addition to his work on polio, Weller also contributed to treatingschistosomiasis, andCoxsackie viruses. He was also the first to isolate the virus responsible forchickenpox.
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