State-Dependent Impulsive Control Strategies for a Tumor-Immune Model

摘要

Controlling the number of tumor cells leads us to expectmore efficient strategies for treatment of tumor. Towards this goal, a tumorimmune model with state-dependent impulsive treatments is established. This model may give an efficient treatment schedule to control tumor's abnormal growth. By using the Poincarémap and analogue of Poincaré criterion, some conditions for the existence and stability of a positive order-1 periodic solution of this model are obtained. Moreover, we carry out numerical simulations to illustrate the feasibility of our main results and compare fixed-time impulsive treatment effects with state-dependent impulsive treatment effects. The results of our simulations say that, in determining optimal treatment timing, themodel with state-dependent impulsive control is more efficient than that with fixed-time impulsive control.