Particle-based simulations of reaction-diffusion processes with Aboria

Abstract: Mathematical models of transport and reactions in biological systems have been traditionally written in terms of partial differential equations (PDEs) that describe the time evolution of population-level variables. In recent years, the use of stochastic particle-based models, which keep track of the evolution of each organism in the system, has become widespread. These models provide a lot more detail than the population-based PDE models, for example by explicitly modelling particle-particle interactions, but bring with them many computational challenges. In this paper we overview Aboria, a powerful and flexible C++ library for the implementation of numerical methods for particle-based models. We demonstrate the use of Aboria with a commonly used model in mathematical biology, namely cell chemotaxis. Cells interact with each other and diffuse, biased by extracellular chemicals, that can be altered by the cells themselves. We use a hybrid approach where particle-based models of cells are coupled with a PDE for the concentration of the extracellular chemical.