A novel explicit scheme for stochastic diffusive SIS models with treatment effects

• A novel stochastic computational scheme is developed to solve a system of stochastic partial differential equations modeling the SIS epidemic. • A compact numerical scheme is proposed to discretize the diffusive terms, ensuring computational efficiency and achieving sixth-order accuracy in space. • The stability of the computational scheme is established through consistency and stability analysis in the mean square sense. • The scheme is applied to a stochastic diffusive SIS model with an incidence rate, effectively capturing spatial disease transmission dynamics. • Numerical experiments demonstrate the scheme’s superior accuracy compared to the Euler and Runge–Kutta methods, providing insights into the effect of treatment rates and infection parameters on disease spread. In this study, we propose a novel computational scheme for solving deterministic and stochastic partial differential equations (PDEs). The scheme is designed as an explicit two-stage method, where only the time-dependent terms are discretized, ensuring computational efficiency. A compact finite difference scheme is employed to discretize the spatial components, achieving a sixth-order accuracy in space. The stability and consistency of the proposed method are thoroughly investigated in the mean square sense, guaranteeing its validity for stochastic PDEs. The scheme's effectiveness is demonstrated by applying it to a stochastic diffusive SIS epidemic model. Furthermore, a comparative analysis uses existing numerical methods for deterministic models, including the Runge–Kutta and Euler schemes. The results indicate that the proposed scheme provides higher accuracy and reduced numerical error, making it a promising approach for solving complex epidemiological models.