Mathematical modeling and cost-effective intervention strategies for diabetes management: A data-driven and numerical analysis approach

Abstract

Diabetes mellitus is a chronic, non-communicable disease that continues to pose a major global health burden. Effective management strategies require not only clinical interventions but also robust modeling frameworks to guide public health decisions. In this study, we develop a compartmental model to describe the dynamics of diabetes under both pharmacological and non-pharmacological interventions. The model is solved using a Nonstandard Finite Difference (NSFD) scheme, which preserves key properties such as positivity and boundedness, and demonstrates superior stability compared to classical numerical methods (RK4 and Forward Euler). The model parameters are estimated by fitting to annual diabetes prevalence data from the United States (2000–2022). A global sensitivity analysis using Partial Rank Correlation Coefficients (PRCC) identifies the most influential parameters driving disease dynamics. To evaluate intervention strategies, the model is extended with three time-dependent control measures, followed by a cost-effectiveness analysis to assess their relative efficiency. Our findings highlight the critical parameters influencing diabetes progression and suggest optimal intervention strategies that balance effectiveness with economic feasibility. These results provide valuable insights for improving diabetes management and support evidence-based public health planning.