In this paper, we consider an epidemic model of Ebola disease which is deadly in its transmission. Local stability analysis of the model equilibria was investigated. We computed the basic reproduction number γ Rγ_0 using the next generation method. The threshold parameter R_0 was found to be dependent on several hosts of model parameters in determining the stability of an invading epidemic into the population. We have numerically described the model trajectories using Matlab. KEYWORDS: Basic Reproduction number, Ebola virus, Next-generation matrix, Local stability analysis
