Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer
Understanding the dynamics of human hosts and tumors is of critical importance. A mathematical model was developed by Bunimovich-Mendrazitsky et al. ([10]), who explored the immune response in bladder cancer as an effect of BCG treatment. This treatment exploits the host's own immune system to...
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AIMS Press
2011-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.529 |
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| author | Svetlana Bunimovich-Mendrazitsky Yakov Goltser |
| author_facet | Svetlana Bunimovich-Mendrazitsky Yakov Goltser |
| author_sort | Svetlana Bunimovich-Mendrazitsky |
| collection | DOAJ |
| description | Understanding the dynamics of human hosts and tumors is of critical importance. A mathematical model was developed by Bunimovich-Mendrazitsky et al. ([10]), who explored the immune response in bladder cancer as an effect of BCG treatment. This treatment exploits the host's own immune system to boost a response that will enable the host to rid itself of the tumor. Although this model was extensively studied using numerical simulation, no analytical results on global tumor dynamics were originally presented. In this work, we analyze stability in a mathematical model for BCG treatment of bladder cancer based on the use of quasi-normal form and stability theory. These tools are employed in the critical cases, especially when analysis of the linearized system is insufficient. Our goal is to gain a deeper insight into the BCG treatment of bladder cancer, which is based on a mathematical model and biological considerations, and thereby to bring us one step closer to the design of a relevant clinical protocol. |
| format | Article |
| id | doaj-art-954ec7eee67b4c8a9bc5c733ee26c806 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-954ec7eee67b4c8a9bc5c733ee26c8062025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018252954710.3934/mbe.2011.8.529Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancerSvetlana Bunimovich-Mendrazitsky0Yakov Goltser1Ariel University Centerof of Samaria, Mathematics Department, ArielAriel University Centerof of Samaria, Mathematics Department, ArielUnderstanding the dynamics of human hosts and tumors is of critical importance. A mathematical model was developed by Bunimovich-Mendrazitsky et al. ([10]), who explored the immune response in bladder cancer as an effect of BCG treatment. This treatment exploits the host's own immune system to boost a response that will enable the host to rid itself of the tumor. Although this model was extensively studied using numerical simulation, no analytical results on global tumor dynamics were originally presented. In this work, we analyze stability in a mathematical model for BCG treatment of bladder cancer based on the use of quasi-normal form and stability theory. These tools are employed in the critical cases, especially when analysis of the linearized system is insufficient. Our goal is to gain a deeper insight into the BCG treatment of bladder cancer, which is based on a mathematical model and biological considerations, and thereby to bring us one step closer to the design of a relevant clinical protocol.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.529nonlinear dynamics.normal formcritical caseimmune responsezero eigenvalue |
| spellingShingle | Svetlana Bunimovich-Mendrazitsky Yakov Goltser Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer Mathematical Biosciences and Engineering nonlinear dynamics. normal form critical case immune response zero eigenvalue |
| title | Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer |
| title_full | Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer |
| title_fullStr | Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer |
| title_full_unstemmed | Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer |
| title_short | Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer |
| title_sort | use of quasi normal form to examine stability of tumor free equilibrium in a mathematical model of bcg treatment of bladder cancer |
| topic | nonlinear dynamics. normal form critical case immune response zero eigenvalue |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.529 |
| work_keys_str_mv | AT svetlanabunimovichmendrazitsky useofquasinormalformtoexaminestabilityoftumorfreeequilibriuminamathematicalmodelofbcgtreatmentofbladdercancer AT yakovgoltser useofquasinormalformtoexaminestabilityoftumorfreeequilibriuminamathematicalmodelofbcgtreatmentofbladdercancer |