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The book aims to provide an introduction to mathematical models
that describe the dynamics of tumor growth and the evolution of
tumor cells. It can be used as a textbook for advanced
undergraduate or graduate courses, and also serves as a reference
book for researchers. The book has a strong evolutionary component
and reflects the viewpoint that cancer can be understood rationally
through a combination of mathematical and biological tools. It can
be used both by mathematicians and biologists. Mathematically, the
book starts with relatively simple ordinary differential equation
models, and subsequently explores more complex stochastic and
spatial models. Biologically, the book starts with explorations of
the basic dynamics of tumor growth, including competitive
interactions among cells, and subsequently moves on to the
evolutionary dynamics of cancer cells, including scenarios of
cancer initiation, progression, and treatment. The book finishes
with a discussion of advanced topics, which describe how some of
the mathematical concepts can be used to gain insights into a
variety of questions, such as epigenetics, telomeres, gene therapy,
and social interactions of cancer cells.
The book shows how mathematical and computational models can be
used to study cancer biology. It introduces the concept of
mathematical modeling and then applies it to a variety of topics in
cancer biology. These include aspects of cancer initiation and
progression, such as the somatic evolution of cells, genetic
instability, and angiogenesis. The book also discusses the use of
mathematical models for the analysis of therapeutic approaches such
as chemotherapy, immunotherapy, and the use of oncolytic viruses.
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