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The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.
List of contents
Introduction.- Well-mixed stochastic reaction kinetics.- Population scaling.- Temporal scaling.- Spatial scaling.- Summary and Outlook.- Mathematical background.
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"The primary audience is graduate students and researchers. ... content would have to be selected and formatted for lectures carefully. It is most suitable for independent study, and is especially useful as a reference text for the foundations of techniques used in current research. The choice of references are excellent and very current: it is a good survey of both the relevant foundations and current state of research ... and would be a useful starting point for a literature review." (Chay Paterson, zbMATH 1467.92005, 2021)
