HIGHLIGHTING COMPLEX UNCERTAINTIES IN AN SIRS-INFECTION SPREADING SYSTEM

This paper introduces a novel stochastic susceptible-infected-recovered-susceptible (SIRS) epidemic model tailored to study transportation-related infections. The model is analyzed both theoretically and computationally, offering new insights into the dynamics of disease spread in interconnected urban environments. Theoretically, we employ a Lyapunov function to establish the existence of a global positive solution and demonstrate that the solution is stochastically ultimately bounded (SUB) and stochastically permanent. Additionally, we derive a crucial sufficient condition to determine when the infectious disease may die out in the two cities under study. In the numerical analysis, we implement two distinct computational methods: the stochastic Euler–Maruyama (SEM) method and the stochastic nonstandard finite difference (SNSFD) method, to validate the theoretical findings of the studied model. When comparing the two numerical methods, our results show that the SNSFD method outperforms the SEM method in preserving key dynamic characteristics, such as positivity, boundedness, and stability, especially for larger temporal step sizes. This comparative analysis highlights the robustness and efficiency of the SNSFD scheme in handling complex stochastic epidemic models. The findings are illustrated with clear and detailed graphs, providing an accessible understanding of the model’s behavior under various parameter configurations. This work contributes to the field by combining theoretical rigor with innovative computational techniques, offering a comprehensive framework for studying transportation-related infectious diseases.