William E Schiesser Livres

Focusing on the numerical integration of reaction-diffusion partial differential equations, this book explores a system inspired by Alan Turing's work, known as the Turing model. It delves into the interplay of chemical reactions and diffusion processes, providing insights into the mathematical frameworks and techniques necessary for solving these complex equations. The text is essential for those interested in mathematical modeling in fields such as biology, chemistry, and physics.

The book explores the intersection of numerical methods and analytical solutions in the context of Partial Differential Equations (PDEs). It highlights the necessity of testing and validating numerical methods against PDEs with known solutions. Recent advancements in analytical solutions, especially traveling wave solutions for nonlinear evolutionary PDEs, are emphasized as crucial for developing robust numerical methods. This synergy between analytical research and numerical validation creates a rich framework for evaluating and enhancing computational techniques in PDE analysis.

The book delves into mathematical modeling of post-myocardial infarction dynamics through six ordinary differential equations (ODEs). It provides a detailed analysis of key dependent variables, including the cell densities of unactivated macrophages, M1, and M2 macrophages, as well as concentrations of interleukins IL10 and IL1, and tumor necrosis factor Ta. This comprehensive approach aims to enhance understanding of the biological processes following a heart attack, utilizing R for analysis.

Focusing on the blood-brain barrier (BBB), this book explores its crucial role in regulating the transfer of oxygen and nutrients from the bloodstream to brain tissue. It delves into the complex interplay between brain metabolism and the circulatory system, highlighting how the BBB impacts brain functionality. Through detailed analysis, the book sheds light on the mechanisms that govern this vital barrier, providing insights into its significance for overall brain health and function.

Focusing on computer-based modeling of COVID-19, this book offers a comprehensive introduction to a five-ordinary differential equation (ODE) model. It includes a complete model statement, detailed discussions of the ODEs, initial conditions, and parameters. A line-by-line explanation of R routines allows readers to execute the code without prior knowledge of numerical algorithms or programming, enabling them to conduct numerical experiments on basic computers. This accessible approach makes it suitable for a wide range of readers interested in epidemiological modeling.

The book presents two distinct models for understanding virus transmission and management. The Lung/Respiratory System Model (LSM) focuses on the physiological aspects of viral spread within the respiratory system, while the SVIR model categorizes populations into susceptible, vaccinated, infected, and recovered groups to analyze dynamics and control strategies. Each model offers unique insights into the mechanisms of viral behavior and potential interventions for public health.

Multiple myeloma is a form of bone cancer. Specifically, it is a cancer of the plasma cells found in bone marrow (bone soft tissue). Normal plasma cells are an important part of the immune system. Mathematical models for multiple myeloma based on ordinary and partial differential equations (ODE/PDEs) are presented in this book, 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 dependent variable components in the bone marrow and peripheral blood: (1) protein produced by multiple myeloma cells, termed the M protein, (2) cytotoxic T lymphocytes (CTLs), (3) natural killer (NK) cells, and (4) regulatory T cells (Tregs). 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 using the R routines that are available through a download. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences.

This book focuses on a mathematical model describing a reduction in oxygen (O2) to the brain resulting from the impaired respiratory function of the lungs caused by COVID-19. The dynamics of blood flow along the brain capillaries and tissue are modeled as systems of ordinary and partial differential equations (ODE/PDEs).