Method for Solving Fuzzy-Stochastic Diffusive SIR-β Systems: Development and Stability Analysis

Abstract

This study presents a novel computational framework for deterministic and stochastic models. A computational scheme is constructed on two-time levels. A compact approach is employed to efficiently manage space-dependent terms, with the initial stage utilizing a modified exponential integrator. The stability and consistency of the scheme in the mean-square sense have also been established. The concept is implemented on a stochastic fuzzy diffusive SIR-β model, which is resolved using three distinct numerical techniques. To assess accuracy and performance, a comparative analysis is performed between the proposed scheme and the current Non-Standard Finite Difference (NSFD) scheme. The findings indicate that the proposed system consistently outperforms the NSFD method, ensuring greater numerical stability and precision in epidemic modelling. The comparison shows that the proposed scheme performs better than the existing non-standard finite difference scheme in most cases.