Dynamic behavior of a stochastic epidemic model for skin sores: theoretical and computational perspectives

The present research work introduces a novel computational approach to the study of a nonlinear stochastic epidemic model for skin sores and also a deterministic model. Theoretical analyzing leads to establishing the existence, positive nature, and boundedness of solutions along with the local stability of equilibria. The application of multiple numeric methods including classical Euler, Runge-Kutta, and Euler-Maruyama methods as well as a stochastic nonstandard finite difference (NSFD) approach together with the model's dynamic behavior exploration is the main method of research for this project. The NSFD scheme stands out for its ability to give better precision and stability in numerical computations, besides being time-efficient and not dependent on the size of the time step. A complete comparison reveals the proposed scheme's capability and consistency in seizing both deterministic and stochastic dynamics of the epidemic system. The results of the study lead to a connection between theoretical analysis and practical computation and still give considerable understanding of the reliable simulations of stochastic epidemic processes.