Dynamics of a stochastic glucose-insulin model with impulsive injection of insulin

In this paper, the dynamics of a stochastic glucose-insulin model with impulsive injection of insulin are investigated analytically and numerically. Firstly, we show that the system admits unique positive global solution starting from the positive initial value, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, according to the theory of Khasminskii, we show that there exists at least one nontrivial positive periodic solution. Finally, numerical simulations are carried out to support our theoretical results. It is found that: (i) The presence of environmental noises is capable of supporting the irregular oscillation of blood glucose level, and the average level of the glucose always increases with the increase in noise intensity. (ii) The higher the volatility of the environmental noises, the more difficult the prediction of the peak size of blood glucose level.