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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 529-547. doi: 10.3934/mbe.2011.8.529
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Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer

  • 1.
    Ariel University Centerof of Samaria, Mathematics Department, Ariel
  • Received: 01 May 2010 Accepted: 29 June 2018 Published: 01 April 2011

  • MSC : Primary: 58F15, 58F17; Secondary: 53C35.

  • 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.

    Citation: 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[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 529-547. doi: 10.3934/mbe.2011.8.529

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  • 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.


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