State-Dependent Impulsive Control Strategies for a Tumor-Immune Model
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 usin...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/2979414 |
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| _version_ | 1832551991542284288 |
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| author | Kwang Su Kim Giphil Cho Lin-Fei Nie Il Hyo Jung |
| author_facet | Kwang Su Kim Giphil Cho Lin-Fei Nie Il Hyo Jung |
| author_sort | Kwang Su Kim |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-01bf367571d345899d49eda49233e531 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-01bf367571d345899d49eda49233e5312025-02-03T05:59:52ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/29794142979414State-Dependent Impulsive Control Strategies for a Tumor-Immune ModelKwang Su Kim0Giphil Cho1Lin-Fei Nie2Il Hyo Jung3Department of Mathematics, Pusan National University, Busan 609-735, Republic of KoreaDepartment of Mathematics, Pusan National University, Busan 609-735, Republic of KoreaCollege of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, ChinaDepartment of Mathematics, Pusan National University, Busan 609-735, Republic of KoreaControlling 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.http://dx.doi.org/10.1155/2016/2979414 |
| spellingShingle | Kwang Su Kim Giphil Cho Lin-Fei Nie Il Hyo Jung State-Dependent Impulsive Control Strategies for a Tumor-Immune Model Discrete Dynamics in Nature and Society |
| title | State-Dependent Impulsive Control Strategies for a Tumor-Immune Model |
| title_full | State-Dependent Impulsive Control Strategies for a Tumor-Immune Model |
| title_fullStr | State-Dependent Impulsive Control Strategies for a Tumor-Immune Model |
| title_full_unstemmed | State-Dependent Impulsive Control Strategies for a Tumor-Immune Model |
| title_short | State-Dependent Impulsive Control Strategies for a Tumor-Immune Model |
| title_sort | state dependent impulsive control strategies for a tumor immune model |
| url | http://dx.doi.org/10.1155/2016/2979414 |
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