Chemotaxis Modeling of Autoimmune Inflammation: PDE Computer Analysis in R

The immune system can deplete macrophages and produce cytokines, which is a counterproductive autoimmune response. This book is directed to the computer-based modeling of chemotaxis inflammation, which is based on a model of three partial differential equations (PDEs). The numerical integration of the PDEs is by the method of lines (MOL), and the three PDE model can be used for computer-based experimentation to enhance a quantitative understanding of a postulated inflammation.

Format: Hardback
Length: 144 pages
Publication date: 21 September 2022
Publisher: Taylor & Francis Ltd

In response to an infection, the immune system can deplete macrophages, specialized white blood cells, and produce cytokines that are pro-inflammatory or anti-inflammatory. This counterproductive autoimmune response is mathematically represented as nonlinear chemotaxis diffusion. This book is directed to the computer-based modeling of chemotaxis inflammation. The spatiotemporal analysis is based on a model of three partial differential equations (PDEs). The three PDE model is coded (programmed) as a set of routines in R, a quality, open-source, scientific programming system. The numerical integration (solution) of the PDEs is by the method of lines (MOL). The three PDE model can be used for computer-based experimentation, for example, parameter variation and changes in the model equations or alternate models, to enhance a quantitative understanding of a postulated inflammation. This experimentation is illustrated by chapters pertaining to: (1) the computation and display of the PDE time derivatives, (2) the RHS terms of the PDEs with emphasis on the chemotaxis terms, (3) parameter variations to demonstrate parameter effects and sensitivities, and (4) additional terms in the PDEs to include PDE coupling and extensions of the basic PDE model.

Weight: 440g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032316062