From Papers of the War Department Transcriptions
The fever that Henry Knox is talking about is the Yellow Fever Epidemic of Philadelphia, which took place in 1793. Philadelphia was the capitol of the United States at the time, and Washington and his advisors (modernly called the Cabinet) worked at 5th and Market Streets.
The spring of 1793 was particularly wet, with many pools of sitting water. The poor drainage systems of the times made the streets flood and overflow with water. Alternatively, the summer of 1793 was very dry.
During the early summer a revolt started in the West Indies causing thousands of people to head to the port of Philadelphia. With them they brought stories of a pestilent fever that had been ravaging the islands. In addition to the stories of the fever, they brought the mosquitos that carried the fever - commonly called yellow fever. The mosquitos bred in the pools of standing water still in the streets and on in the Delaware River.
In mid-August, the first cases of yellow fever occurred. By October over 1,400 people had died from the fever. Before the cold temperatures in November stopped the epidemic there were over 4,000 deaths. Yellow fever derrives its name from the yellow hue that the patients eyes and skin turns when the liver becomes jaundiced.
Alexander Hamilton took ill with the fever in early September and his wife, Elizabeth "Betsy" Hamilton became sick soon after. He and his family retreated to their summer residence, called Fair Hill.
Hamilton's illness was not only important because he was the current Secretary of the Treasury, but because of the physician that he chose to endorse. At the time, Dr. Benjamin Rush was, arguably, the most popular doctor in Philadephia. However, Alexander Hamilton chose to endorse Dr. Edward Stevens. Stevens remedies including administering quinine and bringing down the patient's fever with cool water baths. Conversly, Rush held on to the long standing beliefs that purging the body of the illness and lowering the patient's fever by bleeding up to six quarts of blood.
Sources: Chernow, Ron (2004) "Alexander Hamilton." Penguin Books. London.
Powell, JH (1949) "Bring Out Your Dead: The Great Plague of Yellow Fever in Philadelphia in 1793." Time Reading Program. New York.