Dynamics of Cancer: Mathematical Foundations of Oncology

Understanding Cancer Dynamics: Mathematical Insights and Biological Perspectives

Introduction

This comprehensive volume delves into the intricate world of cancer dynamics, employing mathematical modeling as a lens to decode the underlying complexities. Designed for advanced undergraduate and graduate students, the book also serves as an indispensable reference for researchers in mathematical biology, mathematical oncology, and biology.

Evolutionary Foundations and Mathematical Perspectives

The book approaches cancer through an evolutionary lens, recognizing it as a rational phenomenon explainable through the convergence of mathematical and biological approaches. Beginning with basic ordinary differential equation (ODE) models, the mathematical framework gradually progresses to more advanced stochastic and spatial models.

Biologically, the book embarks on an exploration of tumor growth dynamics, investigating competitive interactions among cells. Subsequently, it ventures into the evolutionary dynamics of cancer cells, including the enigmatic scenarios of cancer initiation, progression, and treatment.

Advanced Applications and Broader Implications

The book concludes with a discussion of advanced topics that demonstrate how mathematical concepts illuminate diverse aspects of cancer, including epigenetics, telomeres, gene therapy, and the social interactions of cancer cells. These insights pave the way for deeper understanding and potential therapeutic interventions.

In-Depth Chapter Coverage

• Teaching Guide: Provides practical guidance for educators utilizing the book in academic settings.
• Cancer and Somatic Evolution: Introduces the fundamental concepts of cancer as a somatic evolutionary process.
• Mathematical Modeling of Tumorigenesis: Outlines the mathematical tools and techniques used to model various aspects of tumor development.
• Basic Growth Dynamics and Deterministic Models: Explores single-species growth, two-species competition, and the implications of chromosomal instability.
• Evolutionary Dynamics and Stochastic Models: Investigates the evolutionary dynamics of tumor initiation and progression, including the role of oncogenes and tumor-suppressor genes.
• Spatial Evolutionary Dynamics: Delves into the spatial aspects of tumor initiation and growth, highlighting the complexities of heterogeneous tumor microenvironments.
• Stochastic Modeling of Cellular Growth, Treatment, and Resistance: Examines the stochastic processes underlying cellular growth, treatment resistance, and the development of drug resistance.
• Advanced Topics: Explores the evolutionary dynamics of stem-cell driven tumor growth, the kinetics of disease progression, epigenetic changes, and the immune response to cancer.

Target Audience

This book is tailored to researchers in mathematical biology, mathematical modeling, biology, and mathematical oncology who seek a comprehensive understanding of cancer dynamics and its mathematical underpinnings.