In this study, a deterministic mathematical model of Ebola transmission is analyzed under random effects. A recent compartmental model of Berge et al. incorporates both direct and indirect transmission in the model. We assume the parameters of this model are normally distributed random variables to investigate the random behavior of disease transmission. Random differential transformation method is used to obtain the approximate expectation of disease recovery. Furthermore, the approximation for expected recovery is modified by using Laplace-Pade method. Comparison of results indicate that the Laplace-Pade modification provides a better approximation. We also interpret the long term random behavior of the disease dynamics using simulation results.