Numerical Study on Stochastic Diabetes Mellitus Model with Additive Noise

Area of Science:

• Mathematical modeling
• Computational mathematics
• Epidemiology

Background:

• Diabetes mellitus poses a significant global health challenge.
• Stochastic models are crucial for understanding disease dynamics with inherent randomness.
• Accurate numerical simulations are vital for predicting disease progression.

Purpose of the Study:

• To perform numerical analysis and simulation of a stochastic diabetes mellitus model with additive noise.
• To establish the existence and uniqueness theorem for the model's solution.
• To investigate the mean square stability and convergence of numerical solutions.

Main Methods:

• Development of a stochastic differential equation model for diabetes mellitus.
• Application of mathematical theorems to prove existence and uniqueness of solutions.
• Numerical simulation techniques to analyze model behavior and stability.
• Convergence analysis of the proposed numerical schemes.

Main Results:

• The existence and uniqueness of the solution for the stochastic diabetes mellitus model were established under specific assumptions.
• The mean square stability and convergence properties of the numerical solutions were proven.
• Numerical computations demonstrated the practical applicability of the theorems.

Conclusions:

• The study provides a rigorous mathematical framework for analyzing stochastic models of diabetes mellitus.
• The established theorems and numerical methods offer reliable tools for forecasting disease trends.
• This work contributes to a better understanding and management of diabetes mellitus through computational approaches.