In this study we propose a modified SEQIR model to further investigate the dynamics of Ebola virus. A deterministic and stochastic framework was considered to verify the implication(s) of saturation coefficient on the transmission dynamics of Ebola. Necessary qualitative analysis: Existence and Uniqueness, boundedness, local and global stability, at disease - free equilibrium were considered to validate the epidemiological feasibility of the model. The reproduction number was found to be less than unity. Furthermore, the effective contact rate of the disease and saturation coefficient rates were varied within the model to validate the effects of these parameters on the transmission dynamics of the infection and results from numerical simulations using assumed (fitted) values indicate the overall effects of the saturation coefficient rate in phasing out the disease in the long run when moderated.