Epidemiology, equilibria, and ebola : a dynamical analysis

Abstract

In order to understand the forces that drive outbreaks such as the recent Ebola outbreak in West Africa, the force of infection must be broken down into a system of di erential equations. With the current understanding of how the equations and diseases interact, it's possible to build diseases from equations and build equations from diseases. Breaking down the di erential equations farther leads to a deeper understanding of what "stability" looks like for a disease and ultimately enables the prediction of the behavior of diseases, including points of peak infection rates and the total number of people a ected by the disease. This paper will break down the mathematics behind compartmental epidemic models and then use them to develop a model which a rms a hopeful future with the decline of Ebola in West Africa so that it may take its place in history as another disease scare that never fully developed.