A Hybrid Finite Difference Approach for Solving Fuzzy Stochastic \(SIR-β\) Model with Diffusion and Incidence Rate

A finite difference scheme is proposed for solving stochastic fuzzy partial differential equations. The scheme is explicit and constructed on two-time levels. The first stage of the scheme is the modified time integrator. The stability and consistency of the scheme in the mean square sense are also provided. The scheme is applied to the mathematical model of stochastic fuzzy SIR- model using incidence rate. The scheme is compared with existing nonstandard finite difference schemes for solving deterministic models. The scheme performs better than the existing nonstandard finite difference method in most compared figures. Using a computationally efficient and robust system, this work develops numerical methods for solving epidemiological models under uncertainty, enabling researchers and lawmakers to improve knowledge and control of infectious diseases.