(untitled) (Contemporary Mathematics, 2025)
This paper investigates the stochastic dynamics of a multi-population epidemiological model using the Milstein method to discretize the governing equations. The model incorporates susceptible, infected, hospitalized, and recovered populations, with noise intensities influencing the transmission dynamics. In the deterministic case, the system exhibits smooth and predictable behavior, with populations converging to equilibrium values. However, the introduction of stochastic noise leads to significant variability in the system dynamics. Low noise intensities result in minimal fluctuations, while high noise levels induce pronounced and extreme stochastic behavior. The infected population is particularly sensitive to noise, with high noise intensities causing destabilization. These findings highlight the critical role of noise in epidemiological modeling and underscore the importance of controlling stochastic effects to maintain system stability.