Mathematical and numerical investigations of fractional stochastic epidemic model

Sexually transmitted diseases are infectious diseases and a significant threat to human health. In this work, a standard integer-order model of Chlamydia is transformed into a fractional-order stochastic mathematical model. The steady-state of the continuous system is determined and considered for disease forecasting and stability analysis. The fractional stochastic system is tested for stability at both equilibrium states by following the classical Jacobian matrix theory. It is investigated the underlying epidemic model has a unique solution. The non-negative and bounded solutions of the model also provide a deeper understanding of the disease propagation. Then, a finite difference numerical algorithm is constructed for approximating the solution. To assess the efficiency of the algorithm, non-negativity and boundedness of the numerical method are investigated. Furthermore, the algorithm is applied to a test example to obtain the simulated graphs. Ultimately, the study's outcomes are summarized in the form of conclusions.