Complex sentence: He took up theories that the mosquito was a vector for malaria, held by John Crawford and his contemporary Lewis Daniel Beauperthy, and is credited as being the first to apply them to yellow fever, then a serious health problem of the American South.
Split into simpler sentences: He took up theories that the mosquito was a vector for malaria, held by John Crawford and his contemporary Lewis Daniel Beauperthy. He is credited as being the first to apply the insect vector theory to yellow fever, then a serious health problem of the American South.