Type-1 diabetes mathematical analysis based on Free Fatty Acids in the presence of insuline

This work is devoted to investigate a six-dimensional mathematical model of first-order ordinary differential equations with the presence of growth hormone. The analysis of the time-behavior dynamics of all state variables is discussed by applying the localization of compact invariant sets method; considering a treatment based on both growth hormone and insulin effects. To the best of our knowledge, this method has not been applied to explore the global dynamic of this phenomenon, and only local asymptotic stability for this particular model has been reported. The mathematical process enhances a reliable strategy to a leading path for preliminary analysis related to other types of in-silico test considerations. Moreover, a closed-loop asymptotic stability analysis by Lyapunov theory is achieved by considering two possible control inputs that could modify the concentration level of insulin and growth hormone. Finally, a discussion about biological implications and numerical simulations are presented.