Comprehensive Study of a Diabetes Mellitus Mathematical Model Using Numerical Methods with Stability and Parametric...

Area of Science:

• Mathematical Biology
• Public Health Modeling
• Epidemiology

Background:

• Diabetes is a global epidemic with significant public health implications.
• Effective monitoring and control strategies are crucial for managing diabetes prevalence and complications.
• Mathematical models offer a valuable tool for understanding and predicting disease progression.

Purpose of the Study:

• To analyze the diabetes complication (DC) mathematical model using various numerical methods.
• To investigate the impact of time step size and model parameters on diabetes progression.
• To provide insights for improving public health strategies for diabetes screening and treatment.

Main Methods:

• Analysis of the DC model using five distinct numerical methods.
• Examination of the influence of time step size on model convergence.
• Parametric analysis to understand the role of different parameters in diabetes complication development.

Main Results:

• The Runge-Kutta (RK) method demonstrated the highest accuracy in modeling diabetes complications.
• Adam-Moulton's method also yielded favorable results for the DC model.
• Parametric analysis highlighted the critical role of specific parameter values in model convergence.

Conclusions:

• The study offers a comprehensive understanding of diabetes complication development post-diagnosis.
• Numerical analysis of the DC model can inform public health policy and intervention strategies.
• Findings support the development of targeted initiatives for diabetes screening and treatment to improve national health outcomes.