Stochastic Modelling of Reaction–Diffusion Processes
Cambridge Texts in Applied Mathematics Series

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.

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.