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The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs) in biomedical science and engineering (BMSE). The book applies DODE/DPDE models to biological/physiological systems through a series of examples. The first chapter has four example DODE applications that illustrate various properties of delayed systems. This discussion is then extended in the second chapter to an introductory DPDE model with the model solution presented as spatiotemporal numerical and 2D and 3D graphical (plotted) output. Subsequent chapters pertain to a series of DPDE BMSE applications. The author facilitates the use of the models with reasonable time and effort on modest computers. The book is intended for medical researchers, medical clinicians, biophysicists, biochemists, biomedical engineers, chemical engineers, applied mathematicians and applied numerical analysts. The book could also be used at the graduate level for Computer Analysis of Delay Differential Equations and Numerical Analysis of Delay Differential Equations courses. R routines are included throughout the text, and readers can access the R compiler (system) from the Internet to execute the downloaded R routines.
Table of Contents
1. Introduction to Delay Ordinary Differential Equations. 2. Introduction to Delay Partial Differential Equations. 3. Hepatitis B Virus DPDE Model. 4. Tumor Induced Angiogenesis. 5. Metastatic Cancer Cell Invasion of Tissue. 6. Subcutaneous Injection of Insulin. 7. Hematopoietic Stem Cells. 8. Drug Eluting Stents. Appendix A1: Functions dss004, dss044.
William E. Schiesser, emeritus professor at Lehigh University. Schiesser is the Emeritus McCann Professor in the chemical and biomolecular engineering department as well as a former professor in the mathematics department. recently authored several books on computer-based solutions to model real-life phenomena, such as the development of Parkinson’s disease. Schiesser holds a Ph.D. from Princeton University and an honorary Sc.D. from the University of Mons, Belgium. He is the author or co-author of numerous books in his field of research on numerical methods and associated software for ordinary, differential-algebraic and partial differential equations (ODE/DAE/PDEs) and the development of mathematical models based on ODE/DAE/PDEs.
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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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