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General Aspects of Modeling Tumor Growth and Immune Response

  • Chapter
A Survey of Models for Tumor-Immune System Dynamics

Abstract

This chapter opens with a summary of the philosophy and methodology of mathematical modeling (Sections 2.1 and 2.2). In Section 2.3 a survey of deterministic diffusion models of spheroid growth is provided. Section 2.4 addresses a particular type of model, based on a predator-prey description of the immune response to cancer illustrating the modeling pro- cess in some detail. This is followed in Section 2.5 by a spatially-dependent approach to the immune response in a one-dimensional system. Section 2.6 is more speculative in nature: the suggestion is made that the concepts of “tunneling” (as used in quantum mechanics) and “catastrophe” may be applicable to both the development of cancer and the effectiveness of the immune response. Two appendices follow on (i) catastrophe theory and (ii) certain mathematical properties of solutions to diffusion equations.

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  1. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, USA

    John A. Adam

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  1. Department of Mathematics, Old Dominion University, Norfolk, Virginia, 23529-0077, USA

    John A. Adam

  2. Dipartimento di Matematica, Politecnico di Torino, 10129, Torino, Italy

    Nicola Bellomo

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Adam, J.A. (1997). General Aspects of Modeling Tumor Growth and Immune Response. In: Adam, J.A., Bellomo, N. (eds) A Survey of Models for Tumor-Immune System Dynamics. Modeling and Simulation in Science, Engineering, & Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8119-7_2

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