In this paper, the authors address an \(\mathfrak {S}\mathbb {I}\mathfrak {R}\) stochastic epidemic model to investigate the spread of infections between two cities through transportation related infection. We begin by proving that there is a unique positive solution, and thereby the model is well posedness. Using Itô formula along with Chebyshev’s inequality and constructing appropriate Lyapunov functions, we establish sufficient conditions for stochastic ultimate boundedness. Furthermore, we demonstrate stochastic permanence under specific constraints on key parameters and noise intensities. Numerical experiments are conducted using scale conjugate gradient neural networks (SCGNNs), showcasing the effectiveness of the proposed computational framework. Overall, this study offers valuable theoretical and numerical insights for understanding epidemic transmission and control in interconnected urban environments.
