Analysis of Linear and Nonlinear Mathematical Models for Monitoring Diabetic Population with Minor and Major Complications

Goni Umar Modu, Yunusa Aliyu Hadejia, Idris Ahmed, Wiyada Kumam, Phatiphat Thounthong

Abstract

A Mathematical analysis of linear and nonlinear models for monitoring diabetic populations with minor and major complications are considered in this work. The equilibrium point of the linear system is shown to be globally asymptotically stable (GAS) using direct Lyapunov method. For the nonlinear model, three positive equilibrium points were obtained and analyzed and only one of the equilibrium points is globally asymptotically stable (GAS), shown using the direct Lyapunov method. Some numerical simulations are carried out to demonstrate the analytical results. It is found that the prevalence/incidence of diabetes is on the rise. Our results are effective in monitoring diabetic populations with minor and major complications and the mathematical methods used in the analysis can be applied in different work. The models can be used to monitor global diabetic populations over time.