Stability analysis and optimal control of a five-state diabetic population model

Abstract

There exists an extensive literature on differential equation models of diabetic population. In this paper, we developed a five-compartmental model of diabetes population dynamics using ordinary differential equations. After discussing the governing equations, the existence and global stability of the system are derived. Then, we used the parameter estimation to estimate the model parameter with the Malaysian diabetic projection data. Considering the undiagnosed, diagnosed diabetic with and without complications, which measures the total diabetic prevalence, we obtain the estimated parameter of the curve fit. By this parameter values, we compute the forward index sensitivity for 1% single parameter perturbation. From the index sensitivity point of view, an optimal control problem is theoretically and numerically investigated. Finally, it is numerically shown that the total number of diabetes can be suppressed effectively by implementing an optimal control strategy.

Subject Classification:

• 92B05
• 34D32
• 35B35

Keywords:

• Diabetes
• Diabetic
• Sensitivity
• Stability
• Optimal control