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Mathematical Modelling of Combined Intervention Strategies for the Management and Control of Plasma Glucose of a Diabetes Mellitus Patient: A System Dynamic Modelling Approach

Author

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  • Vincent O. Omwenga

    (School of Computing and Engineering Science, Strathmore University, Nairobi 59857-00200, Kenya)

  • Vaishnav Madhumati

    (Samatvam Endocrinology Diabetes Centre, Bangalore 560041, India)

  • Kumar Vinay

    (Center for Nano Science and Engineering, Indian Institute of Science, Bangalore 560012, India)

  • Sathyanarayan Srikanta

    (Samatvam Endocrinology Diabetes Centre, Bangalore 560041, India)

  • Navakanta Bhat

    (Samatvam Endocrinology Diabetes Centre, Bangalore 560041, India)

Abstract

With the rapid increase of diabetes mellitus cases in the world, management and control of the disease has become a complex and highly dynamic process. This challenge requires a multifaceted approach to manage and control the complications associated with the hyperglycaemia or hypoglycaemia conditions. This paper presents a mathematical model for determining the influence of combined intervention strategies in the management and control for the plasma glucose of the type II diabetes. System dynamics (SD) techniques were used in modelling the sub-compartments of biological systems of an Identifiable Patient (IP). The system dynamic model developed gave an illustration on how typical glucose-insulin dynamics occur at different intervention strategies involving varying amounts of carbohydrates taken, intensity of physical exercises, stress levels and the amount of exogenous insulin administered. The model was conceptualized within a semi-closed loop system representing the patient ecosystem by extending the Bergman Minimal Model. Stochastic differential equations (SDE) were used to capture the non-linear, continuous time varying interactions of the measurements associated with plasma glucose-insulin dynamics. The estimated results from the model showed combined intervention strategies of reduced amounts of carbohydrates intake, reduced stress levels and varying moderately high-to-low exercise intensity at a constant unit of exogenous insulin produced good plasma glucose levels control.

Suggested Citation

  • Vincent O. Omwenga & Vaishnav Madhumati & Kumar Vinay & Sathyanarayan Srikanta & Navakanta Bhat, 2023. "Mathematical Modelling of Combined Intervention Strategies for the Management and Control of Plasma Glucose of a Diabetes Mellitus Patient: A System Dynamic Modelling Approach," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:306-:d:1027826
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    References listed on IDEAS

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    1. Ganjar Alfian & Muhammad Syafrudin & Norma Latif Fitriyani & Muhammad Anshari & Pavel Stasa & Jiri Svub & Jongtae Rhee, 2020. "Deep Neural Network for Predicting Diabetic Retinopathy from Risk Factors," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    2. Omer Mujahid & Ivan Contreras & Aleix Beneyto & Ignacio Conget & Marga Giménez & Josep Vehi, 2022. "Conditional Synthesis of Blood Glucose Profiles for T1D Patients Using Deep Generative Models," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    3. Jones, A.P. & Homer, J.B. & Murphy, D.L. & Essien, J.D.K. & Milstein, B. & Seville, D.A. & Barnes, K., 2006. "Understanding diabetes population dynamics through simulation modeling and experimentation," American Journal of Public Health, American Public Health Association, vol. 96(3), pages 488-494.
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