Dynamics of Cancer

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.Contents:



Teaching Guide
Cancer and Somatic Evolution
Mathematical Modeling of Tumorigenesis


Basic Growth Dynamics and Deterministic Models:

Single Species Growth
Two-Species Competition Dynamics
Competition Between Genetically Stable and Unstable Cells
Chromosomal Instability and Tumor Growth
Angiogenesis Inhibitors, Promoters, and Spatial Growth


Evolutionary Dynamics and Stochastic Models:

Evolutionary Dynamics of Tumor Initiation Through Oncogenes: The Gain-of-Function Model
Evolutionary Dynamics of Tumor Initiation Through Tumor-Suppressor Genes: The Loss-of-Function Model and Stochastic Tunneling
Microsatellite and Chromosomal Instability in Sporadic and Familial Colorectal Cancers
Evolutionary Dynamics in Hierarchical Populations
Spatial Evolutionary Dynamics of Tumor Initiation
Complex Tumor Dynamics in Space
Stochastic Modeling of Cellular Growth, Treatment, and Resistance Generation
Evolutionary Dynamics of Drug Resistance in Chronic Myeloid Leukemia


Advanced Topics:

Evolutionary Dynamics of Stem-Cell Driven Tumor Growth
Tumor Growth Kinetics and Disease Progression
Epigenetic Changes and the Rate of DNA Methylation
Telomeres and Cancer Protection
Gene Therapy and Oncolytic Virus Therapy
Immune Responses, Tumor Growth, and Therapies
Towards Higher Complexities: Social Interactions





Readership: Researchers in mathematical biology, mathematical modeling, biology, mathematical oncology.