Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth
In order to investigate the effect of T cells on inhibiting the tumor growth, based on the limitation of T cell immune recognition，we construct a T cell immune saturation recognition model with time delay Using the transformation rate, the attack rate of T cells, and the activation time delay as thr...
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Harbin University of Science and Technology Publications
2020-04-01
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| Series: | Journal of Harbin University of Science and Technology |
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| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1761 |
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| author | WANG Jingnan LU Lanfen YANG Dezhong ZHANG Yanqiao |
| author_facet | WANG Jingnan LU Lanfen YANG Dezhong ZHANG Yanqiao |
| author_sort | WANG Jingnan |
| collection | DOAJ |
| description | In order to investigate the effect of T cells on inhibiting the tumor growth, based on the limitation of T cell immune recognition，we construct a T cell immune saturation recognition model with time delay Using the transformation rate, the attack rate of T cells, and the activation time delay as three main parameters, the existence and stability conditions of nontumor equilibrium and positive equilibrium point of tumors are obtained Though the theories of norm form and the central manifold, we obtain the norm form of this model, the critical conditions of undergoing Hopf bifurcation and the properties of the Hopf bifurcation Matlab numerical simulations are performed to show the phenomena of notumor and tumor periodic solution of the system At the same time, we compare the difference of the critical value of time delay between the model with saturated function and the model with bilinear function when the model undergoes Hopf bifurcation under the same conditions Some theoretical methods for T cells inhibiting the growth of tumors are revealed |
| format | Article |
| id | doaj-art-aadbe26fff2444b8bdb193b590965a63 |
| institution | DOAJ |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2020-04-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-aadbe26fff2444b8bdb193b590965a632025-08-20T03:03:03ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832020-04-01250213013710.15938/j.jhust.2020.02.018Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor GrowthWANG Jingnan0LU Lanfen1YANG Dezhong2ZHANG Yanqiao3School of Sciences，Harbin University of Science and Technology，Harbin 150080，ChinaSchool of Sciences，Harbin University of Science and Technology，Harbin 150080，ChinaSchool of Sciences，Harbin University of Science and Technology，Harbin 150080，ChinaDepartment No8 of Internal Medicine，The Affiliated Tumor Hospital of Harbin Medical University，Harbin 150081，ChinaIn order to investigate the effect of T cells on inhibiting the tumor growth, based on the limitation of T cell immune recognition，we construct a T cell immune saturation recognition model with time delay Using the transformation rate, the attack rate of T cells, and the activation time delay as three main parameters, the existence and stability conditions of nontumor equilibrium and positive equilibrium point of tumors are obtained Though the theories of norm form and the central manifold, we obtain the norm form of this model, the critical conditions of undergoing Hopf bifurcation and the properties of the Hopf bifurcation Matlab numerical simulations are performed to show the phenomena of notumor and tumor periodic solution of the system At the same time, we compare the difference of the critical value of time delay between the model with saturated function and the model with bilinear function when the model undergoes Hopf bifurcation under the same conditions Some theoretical methods for T cells inhibiting the growth of tumors are revealedhttps://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1761stumor immune controlstabilityhopf bifurcationperiodic solutioneffect activation time delay |
| spellingShingle | WANG Jingnan LU Lanfen YANG Dezhong ZHANG Yanqiao Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth Journal of Harbin University of Science and Technology stumor immune control stability hopf bifurcation periodic solution effect activation time delay |
| title | Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth |
| title_full | Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth |
| title_fullStr | Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth |
| title_full_unstemmed | Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth |
| title_short | Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth |
| title_sort | hopf bifurcation of delayed tumor t cell immune system and inhibition of tumor growth |
| topic | stumor immune control stability hopf bifurcation periodic solution effect activation time delay |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1761 |
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