Multiscale reaction-diffusion modelling: Application to stochastic front propagation

Martin Robinson
Mathematical Institute
University of Oxford
Oxford, United Kingdom


In this talk, I will discuss multiscale reaction-diffusion modelling and its implementation in Tyche, a Python and C++ software library available at Tyche is designed to be used either stand-alone or included in existing packages, and has recently been incorporated into the popular Smoldyn spatial stochastic simulator ( Tyche implements the Adaptive Two-regime Method (ATRM), a hybrid algorithm suitable for the efficient modelling of stochastic reaction-diffusion systems using both off-lattice and lattice-based models where they are most appropriate.

I will present a case study, using the ATRM for the study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in terms of the Fisher equation, a popular travelling wave model that is used in areas such as gene proliferation, invasive species, combustion and crystallization. Stochastic fluctuations at the leading edge of the wavefront can cause significant reductions in wave speed that are not predicted by the mean-field model. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost.