Stochastic Modelling of Reaction–Diffusion Processes

Radek Erban (University of Oxford), S. Jonathan Chapman (University of Oxford)

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English

Cambridge University Press
30 January 2020

Probability & statistics; Mathematical modelling

Series: Cambridge Texts in Applied Mathematics

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

By: Radek Erban (University of Oxford), S. Jonathan Chapman (University of Oxford)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 158mm, Spine: 18mm
Weight: 600g
ISBN: 9781108498128
ISBN 10: 1108498124
Series: Cambridge Texts in Applied Mathematics
Pages: 319
Publication Date: 30 January 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Stochastic simulation of chemical reactions; 2. Deterministic versus stochastic modelling; 3. Stochastic differential equations; 4. Diffusion; 5. Efficient stochastic modelling of chemical reactions; 6. Stochastic reaction-diffusion models; 7. SSAs for reaction-diffusion-advection processes; 8. Microscopic models of Brownian motion; 9. Multiscale and multi-resolution methods; Appendix A. Deterministic modelling of chemical reactions; Appendix B. Discrete probability distributions; Appendix C. Continuous probability distributions; References; Index.

Radek Erban is Professor of Mathematics at the University of Oxford, a Fellow of Merton College, Oxford and a Royal Society University Research Fellow. S. Jonathan Chapman is Professor of Mathematics and its Applications at the University of Oxford, and a Fellow of Mansfield College, Oxford.

Reviews for Stochastic Modelling of Reaction–Diffusion Processes

'The text can be used effectively for solitary study or as a textbook for a course offered at the boundary between undergraduate and beginning graduate study ... This is a remarkable, even admirable, work that bears the mark of its Oxford origins. Its potential audience includes chemists and mathematicians as well as adventuresome biologists and physicists and perhaps even bright or intrepid general readers.' A. E. Viste, Choice 'This textbook is an example-driven introduction to stochastic modeling in mathematical biology ... Beyond serving as a course textbook, the book could serve as a good general introduction to the area of stochastic modeling in biology for researchers, particularly given the copious citations to more specialist texts.' Andrew Krause, MAA Reviews 'Erban and Chapman's Stochastic Modelling of Reaction-Diffusion Processes will be valuable both as a reference for practitioners and as a textbook for a graduate course on stochastic modelling. Every chapter includes problems for the reader. The problems are well written and appropriate for most intended readers of the book. I hope that this book is widely adopted and that it becomes a standard textbook in the field.' Michael A. Salins, Mathematical Reviews/MathSciNet Review