Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy
A fractional-order tumor-immune interaction model with immunotherapy is proposed and examined. The existence, uniqueness, and nonnegativity of the solutions are proved. The local and global asymptotic stability of some equilibrium points are investigated. In particular, we present the sufficient con...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/7062957 |
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| _version_ | 1849467853286146048 |
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| author | Wenbin Yang Xiaozhou Feng Shuhui Liang Xiaojuan Wang |
| author_facet | Wenbin Yang Xiaozhou Feng Shuhui Liang Xiaojuan Wang |
| author_sort | Wenbin Yang |
| collection | DOAJ |
| description | A fractional-order tumor-immune interaction model with immunotherapy is proposed and examined. The existence, uniqueness, and nonnegativity of the solutions are proved. The local and global asymptotic stability of some equilibrium points are investigated. In particular, we present the sufficient conditions for asymptotic stability of tumor-free equilibrium. Finally, numerical simulations are conducted to illustrate the analytical results. The results indicate that the fractional order has a stabilization effect, and it may help to control the tumor extinction. |
| format | Article |
| id | doaj-art-e0a062162dac448da59186e521bdf737 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e0a062162dac448da59186e521bdf7372025-08-20T03:26:00ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/70629577062957Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with ImmunotherapyWenbin Yang0Xiaozhou Feng1Shuhui Liang2Xiaojuan Wang3School of Science, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, ChinaSchool of Science, Xi’an Technological University, Xi’an, Shaanxi 710032, ChinaXijing Hospital of Digestive Diseases, Xijing Hospital, Air Force Medical University of PLA, Xi’an, Shaanxi 710032, ChinaXijing Hospital of Digestive Diseases, Xijing Hospital, Air Force Medical University of PLA, Xi’an, Shaanxi 710032, ChinaA fractional-order tumor-immune interaction model with immunotherapy is proposed and examined. The existence, uniqueness, and nonnegativity of the solutions are proved. The local and global asymptotic stability of some equilibrium points are investigated. In particular, we present the sufficient conditions for asymptotic stability of tumor-free equilibrium. Finally, numerical simulations are conducted to illustrate the analytical results. The results indicate that the fractional order has a stabilization effect, and it may help to control the tumor extinction.http://dx.doi.org/10.1155/2020/7062957 |
| spellingShingle | Wenbin Yang Xiaozhou Feng Shuhui Liang Xiaojuan Wang Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy Complexity |
| title | Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy |
| title_full | Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy |
| title_fullStr | Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy |
| title_full_unstemmed | Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy |
| title_short | Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy |
| title_sort | asymptotic behavior analysis of a fractional order tumor immune interaction model with immunotherapy |
| url | http://dx.doi.org/10.1155/2020/7062957 |
| work_keys_str_mv | AT wenbinyang asymptoticbehavioranalysisofafractionalordertumorimmuneinteractionmodelwithimmunotherapy AT xiaozhoufeng asymptoticbehavioranalysisofafractionalordertumorimmuneinteractionmodelwithimmunotherapy AT shuhuiliang asymptoticbehavioranalysisofafractionalordertumorimmuneinteractionmodelwithimmunotherapy AT xiaojuanwang asymptoticbehavioranalysisofafractionalordertumorimmuneinteractionmodelwithimmunotherapy |