Abstract
Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in deterministic and stochastic senses. An essential tool, Euler-Maruyama, is studied for the solution of said model. Standard and nonstandard evolutionary approaches are presented for the stochastic model in terms of efficiency and low-cost approximations. The standard evolutionary procedures like stochastic Euler-Maruyama and stochastic Runge-Kutta fail to restore the essential features of biological problems. On the other hand, the proposed method is efficient, of meager cost, and adopts all the desired feasible properties. At the end of this paper the comparison section is presented to support efficient analysis.