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<p>Type 2 diabetes is a chronic metabolic disorder characterized by persistent hyperglycemia due to insulin resistance and progressive metabolic dysfunction. Beyond clinical management, diabetes represents a major public health challenge, especially in countries experiencing rapid urbanization and lifestyle transitions. This study proposes a four-dimensional compartmental model describing the progression of diabetes through successive metabolic stages. The system is shown to be competitive and to admit a unique positive equilibrium, whose global asymptotic stability is established. A cumulative progression index <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> is defined to characterize the expected advancement toward severe complications and to serve as a heuristic threshold for long-term disease persistence. Numerical simulations calibrated with Algerian data illustrate distinct dynamical regimes and highlight the intrinsic tendency of the population to progress to advanced stages. The model is then extended to an optimal control framework, incorporating lifestyle and pharmacological interventions, which provides a decision-support tool for evaluating intervention intensity, timing, and combination strategies. This framework offers a mathematically consistent and operationally relevant approach to assist policymakers in planning and managing chronic metabolic disorders under resource constraints.</p>

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Dynamic Modeling and Optimal Control of Type 2 Diabetes: An Application to Algerian Data

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • K. Belkhodja,
  • A. Rahmoun

摘要

Type 2 diabetes is a chronic metabolic disorder characterized by persistent hyperglycemia due to insulin resistance and progressive metabolic dysfunction. Beyond clinical management, diabetes represents a major public health challenge, especially in countries experiencing rapid urbanization and lifestyle transitions. This study proposes a four-dimensional compartmental model describing the progression of diabetes through successive metabolic stages. The system is shown to be competitive and to admit a unique positive equilibrium, whose global asymptotic stability is established. A cumulative progression index \(R_0\) R 0 is defined to characterize the expected advancement toward severe complications and to serve as a heuristic threshold for long-term disease persistence. Numerical simulations calibrated with Algerian data illustrate distinct dynamical regimes and highlight the intrinsic tendency of the population to progress to advanced stages. The model is then extended to an optimal control framework, incorporating lifestyle and pharmacological interventions, which provides a decision-support tool for evaluating intervention intensity, timing, and combination strategies. This framework offers a mathematically consistent and operationally relevant approach to assist policymakers in planning and managing chronic metabolic disorders under resource constraints.