Tumour evolution is a complex process involving many different phenomena. Mathematical modelling and computer simulations can help us understand these phenomena, but their development requires a multidisciplinary background-one that includes an understanding of the biological phenomena involved and knowledge of the mathematical techniques used to obtain both qualitative and quantitative results.

Cancer Modelling and Simulation builds the requisite biological foundation and presents the mathematical models and methods most useful for understanding the dynamics of tumour development and growth. In chapters contributed by an interdisciplinary team of leading researchers, this book addresses the entire modelling process, from phenomenological observation to simulation and validation, through the development of mathematical models and their qualitative and quantitative study.

This treatment effectively links the analytical, mathematical, and biological aspects of tumour growth modelling to provide researchers from multiple disciplines with the common language and practical knowledge they need to break down the barriers that can hamper interdisciplinary research. Cancer Modelling and Simulation is an important contribution to the field that undoubtedly will stimulate and remain a valuable reference for continued research for many years.

Deepen students' understanding of biological phenomena

Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material.

New to the Second Edition

• A section on spiral waves
• Recent developments in tumor biology
• More on the numerical solution of differential equations and numerical bifurcation analysis
• MATLAB(r) files available for download online
• Many additional examples and exercises

This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincare phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator-prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases."