Yellow fever is a viral hemorrhagic fever transmitted by the Aedes aegypti mosquito. It has historically caused thousands of deaths throughout Africa, the Americas, Europe, and the Caribbean and continues to pose threats in Africa and Central and South America. The disease is most detrimental in densely populated areas with warmer climates where individuals have limited access to health care facilities. These conditions are exemplified by the yellow fever epidemic of 1878 in Memphis, Tennessee. The limited medical knowledge, warm climate, and densely populated urban areas greatly contributed to the magnitude of the epidemic that killed thousands. We have developed an ordinary differential equations model to simulate the dynamics of human and mosquito populations during a yellow fever outbreak using historical data. Additionally, we examined the use of insect repellent and vaccination as methods to reduce the severity of the outbreak. We examined the conditions under which the disease-free equilibria are stable for the complete model. We also used uncertainty and sensitivity analyses to quantify the reduction in cumulative infections and deaths due to the use of insect repellent and vaccination among humans.