Stochastic Analysis and Stability of Diabetic Population Dynamics

Modeling diabetic illness with random perturbations is the goal of this work. The proposed model consists of three classes: the pre-diabetic population, the diabetic population with complications, and the diabetic population without complications. We examined the suggested problem to determine at least one unique solution within the positive feasible region. The stationary distribution of this model was also explored, and the non-negative C2-Lyapunov function was used to create an adequate condition for the persistence of one stationary ergodic distribution. For this model, the existence and uniqueness of the solution were also established. Additionally, the stochastic non-standard finite difference (NSFD) scheme was developed for the model. The consistency and stability of the scheme were analyzed, showing that it is consistent and stable in the mean-square sense. The underlying system admits a unique endemic equilibrium point. Finally, a test problem was studied by using a numerical technique, varying the noise levels, and maintaining the same parameter values. The outcomes for each stated class were numerically simulated in order to validate our proposed approach.