Modeling and Simulation of Epidemics Using q-Diffusion-Based SEIR Framework with Stochastic Perturbations

The numerical approximation of stochastic partial differential equations (SPDEs), particularly those including q-diffusion, poses considerable challenges due to the requirements for high-order precision, stability amongst random perturbations, and processing efficiency. Because of their simplicity, conventional numerical techniques like the Euler-Maruyama method are frequently employed to solve stochastic differential equations; nonetheless, they may have low-order accuracy and lower stability in stiff or high-resolution situations. This study proposes a novel computational scheme for solving SPDEs arising from a stochastic SEIR model with q-diffusion and a general incidence rate function. A proposed computational scheme can be used to solve stochastic partial differential equations. For spatial discretization, a compact scheme is chosen. The compact scheme can provide a sixth-order accurate solution. The proposed scheme can be considered an extension of the Euler Maruyama method. Stability and consistency in the mean square sense are also provided. For application purposes, the stochastic SEIR model is considered using q-diffusion effects. The scheme is used to solve the stochastic model and compared with the Euler-Maruyama method. The scheme is also compared with nonstandard finite difference method for solving deterministic models. In both cases, it performs better than existing schemes. Incorporating q-diffusion further enhanced the model’s ability to represent realistic spatial-temporal disease dynamics, especially in scenarios where classical diffusion is insufficient.