Delay models of glucose-insulin systems: global stability and oscillated solutions conditional on delays

Recently P. Palumbo, S. Panunzi and A. De Gaetano analyzed a delay model of the glucose-insulin system. They proved its persistence, the existence of a unique positive equilibrium point, as well as the local stability of this point. In this paper we consider further the uniform persistence of such equilibrium solutions and their global stability. Using the omega limit set of a persistent solution and constructing a full time solution, we also investigate the effect of delays in connection with the behavior of oscillating solutions to the system. The model is shown to admit global stability under certain conditions of the parameters. It is also shown that the model admits slowly oscillating behavior, which demonstrates that the model is physiologically consistent and actually applicable to diabetological research.