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Modeling Colorectal Cancer: A Stability Analysis Approach
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Author(s): Svetoslav Nikolov (University of Rostock, Germany & Institute of Mechanics and Biomechanics, Bulgaria), Mukhtar Ullah (University of Rostock, Germany), Momchil Nenov (Institute of Mechanics and Biomechanics, Bulgaria), Julio Vera Gonzalez (University of Rostock, Germany), Peter Raasch (University of Rostock, Germany)and Olaf Wolkenhauer (University of Rostock, Germany)
Copyright: 2013
Pages: 23
Source title:
Medical Advancements in Aging and Regenerative Technologies: Clinical Tools and Applications
Source Author(s)/Editor(s): Andriani Daskalaki (Max Planck Institute for Molecular Genetics, Germany)
DOI: 10.4018/978-1-4666-2506-8.ch003
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Abstract
Mathematical modeling is increasingly used to improve our understanding of colorectal cancer. In the first part of this chapter, the authors give a review of systems biology approaches to investigate colorectal cancer. In the second part, the mathematical model proposed by Johnston et al. (2007) is expanded to include time delays and analysed for its stability. For both models, the original and the extended version, the authors obtain the necessary and sufficient conditions for stability. This is confirmed by numerical simulations. Thus, some new mathematical and biological results are obtained.
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