Wester, Thomas. 2015. Analysis and Simulation of a Mathematical Model of Ebola Virus Dynamics in vivo. Undergraduate thesis. U.S. Naval Academy, Annapolis MD USA. 21 pp.
Abstract: Ebola is known to evade detection by the immune system during infection. In this paper, we use mathematical modeling as a tool to investigate and analyze the immune system dynamics in the presence of Ebola virus infection. The resulting model is a system of non-linear ordinary differential equations derived from known biological dynamics and a few biologically reasonable assumptions. In this paper, we prove existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations. In addition, we derive the viral and immune reproduction numbers, and analyze the local asymptotic stability of the differential equation model. Furthermore, we run numerical simulations to illustrate the impact the variation of the parameters has on the behavior of the system. The analysis we develop provides thresholds for both determining the persistence and elimination of Ebola virus from the immune system, and represents the known biological dynamics of Ebola virus infection.
Keywords: mathematical modeling, ebola virus, stability, numerical simulations
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