The Mathematical Modeling of Diabetic Population with the Formulation of Optimal Control Strategies
Dawodu, K. A.
Department of Mathematical Sciences, The Federal University of Technology, Akure, Ondo State, Nigeria.
Aje, T. *
Department of Mathematical Sciences, The Federal University of Technology, Akure, Ondo State, Nigeria.
Afolabi A. S.
Department of Mathematical Sciences, The Federal University of Technology, Akure, Ondo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this research, a robust mathematical model is formulated to capture both type-1 and type-2 diabetes mellitus progression among children and adults, accounting for cases with and without control measures. The effects of these control interventions on diabetic dynamics are explored, and the efficacy of the outlined strategies is assessed. In the optimal control formulation, Pontryagin’s maximum (or minimum) principle is employed to derive optimal control characterizations, while the Runge-Kutta forward-backward sweep algorithm is applied for numerical simulations of state and adjoint variables. This study demonstrates that the number of advanced-stage diabetic patients and the inherent costs of managing diabetic progression can be minimized. The findings of this research offer valuable insights for policymakers and healthcare professionals in improving diabetes mellitus management.
Keywords: Diabetes mellitus, mathematical model, simulation, optimal control