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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 2979414, 10 pages
Research Article

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

1Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea
2College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

Received 23 May 2016; Accepted 1 September 2016

Academic Editor: Ryusuke Kon

Copyright © 2016 Kwang Su Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Controlling the number of tumor cells leads us to expect more efficient strategies for treatment of tumor. Towards this goal, a tumor-immune 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 Poincaré map 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, the model with state-dependent impulsive control is more efficient than that with fixed-time impulsive control.