Analysis of the mathematical model’s stability describing the prevalence of obesity and its role in diabetes

We propose a continuous-time dynamic epidemiological model that describes the prevalence of obesity in a population and examines the relationship between weight gain and the development of diabetes‎, ‎particularly type~2 diabetes‎. We investigate both the local and global stability of the disease-free and endemic equilibrium points using the Routh--Hurwitz criteria and the construction of appropriate Lyapunov functions‎. ‎Furthermore‎, ‎a sensitivity analysis of the basic reproduction number $R_{0}$ is carried out to determine the relative impact of each model parameter‎. ‎ Numerical simulations performed using MATLAB are presented to illustrate the dynamical behavior of the proposed model‎. The simulation results are consistent with and support the theoretical findings‎.