Abstract
The primary purpose of this study is to perform the comparison of deterministic and stochastic modeling. The effect of threshold number is also observed in this model. For numerical simulations, we have developed some stochastic explicit approaches, but they are dependent on time step size. The implicitly driven explicit approach has been developed for a stochastic meme model. The proposed approach is always independent of time step size. Also, we have presented theorems in support of convergence of the proposed approach for the stochastic meme model.