The problem in the book Fever 1793 is the outbreak of Yellow Fever in Philadelphia in the year 1793. This epidemic infected and killed about 10% of the population, which at the time was about 40,000, so 4,000 people died from the fever. At the time, people, even doctors did not really know how to treat the disease. Dr. Benjamin Rush, one of the most noted doctors in Philadelphia, he was a signer of the Declaration of Independence, was using the antiquated method of bleeding patients.
This process, where a patient suffering from Yellow Fever, weak and drained from the disease, required a doctor to cut the vein of the person and have their blood drip into a bowl until the doctor thought that enough of the disease was removed from the person. Unfortunately this method killed more people than it saved because draining the blood of really weak, sick people only made them more weak.
The disease kept a strangle hold on Philadelphia throughout the summer, many rich families fled the city and went into the country, even though they did not understand how the fever was transmitted. They only knew that if you got it, you would suffer terribly and probably die. They did not know that it was spread by the bite of mosquitoes.
So the problem, the spread of the fever, is narrated through the experience of Mattie Cook and her family. She gets the fever, but survives, because she is treated by French doctors who believe in rest, fluids and herbal medicines to cure the patient.
The problem is solved, the fever subsides and stops infecting people, once the frost of October and November sets in, and all the mosquitoes die off. The people understood that once the frost arrived that the infection rate would slow down and stop, but did not understand how the frost stopped the fever.