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\section{Introduction}  News of the most recent outbreak of yellow fever passing 300 deaths in Angola has prompted fears of the World Health Organisation (WHO) regarding its epidemic progression. Vaccination in some areas regions  of the outbreak are very hard to accomplish, as the process of vaccinating is both very expensive, and hard to enforce on a population to satisfy the necessary threshold (to be explained later). Tracking and predicting progression of disease has always been a difficult aim to accomplish. However, there are several mathematical models that may assist with this problem. These models will be explained and adapted to accommodate a range of underlying assumptions about the population and the method of transforming the disease, which will enable the research question to be answered. This is certainly area that is worthy of exploration, both personally and on a greater scale. I have been an avid follower of how diseases have captivated the attention of global media and prevention efforts, namely the Ebola virus and the Zika virus. I have specifically chosen the Yellow Fever virus as it is a currently developing situation, and has manageable statistics for an exploration of this magnitude.