Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy

K. E.  Starkov; Svetlana Bunimovich-Mendrazitsky; K. E.  Starkov; Svetlana Bunimovich-Mendrazitsky

doi:10.3934/mbe.2016030

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 5: 1059-1075. doi: 10.3934/mbe.2016030

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Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy

1.
Instituto Politecnico Nacional, CITEDI, Avenida IPN N 1310, Nueva Tijuana, Tijuana, BC 22435
2.
Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, 40700

Received: 01 October 2015 Accepted: 29 June 2018 Published: 01 October 2016
MSC : Primary: 58F15, 58F17; Secondary: 53C35.

Understanding the global interaction dynamics between tumor and the immunesystem plays a key role in the advancement of cancer therapy.Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for thestudy of the immune system response to combined therapy for bladder cancerwith Bacillus Calmette-Guérin (BCG) and interleukin-2 (IL-2) . Weutilized a mathematical approach for bladder cancer treatment model forderivation of ultimate upper and lower bounds and proving dissipativityproperty in the sense of Levinson. Furthermore, tumor clearance conditionsfor BCG treatment of bladder cancer are presented. Our method is based onlocalization of compact invariant sets and may be exploited for a predictionof the cells populations dynamics involved into the model.

Keywords:

Citation: K. E. Starkov, Svetlana Bunimovich-Mendrazitsky. Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy[J]. Mathematical Biosciences and Engineering, 2016, 13(5): 1059-1075. doi: 10.3934/mbe.2016030

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Abstract

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