In 1878, thousands in Memphis were killed during an outbreak of yellow fever, a viral hemorrhagic fever transmitted by the Aedes aegypti mosquito, which has affected regions including North and South America, Europe, Africa, and the Caribbean. This disease still affects individuals in Africa and Central and South America. We have developed a mathematical model consisting of nine ordinary differential equations which describe the dynamics of the human and mosquito populations during a yellow fever epidemic. Our model investigates the effects that treatment and removal of standing water have on a mosquito population and consequently a yellow fever epidemic. We have examined the stability of the disease-free equilibrium and the conditions under which the disease-free equilibrium is stable.