ODE/PDE analysis of multiple myeloma : programming in R

Includes bibliographical references and index.

"The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models for multiple myeloma, a form of bone cancer. The models are stated as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples, starting with a basic ODE model in chapter 1, and concluding with a detailed ODE/PDE model in chapter 4 that gives the spatiotemporal distribution of four components in the bone marrow and peripheral blood. The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the multiple myeloma models, such as changes in the ODE/PDE parameters (constants) and form of the model equations"--