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Mathematical models of transport and reactions in biological systems havebeen traditionally written in terms of partial differential equations (PDEs)that describe the time evolution of population-level variables. In recentyears, the use of stochastic particle-based models, which keep track of theevolution of each organism in the system, has become widespread. These modelsprovide a lot more detail than the population-based PDE models, for example byexplicitly modelling particle-particle interactions, but bring with them manycomputational challenges. In this paper we overview Aboria, a powerful andflexible C++ library for the implementation of numerical methods forparticle-based models. We demonstrate the use of Aboria with a commonly usedmodel in mathematical biology, namely cell chemotaxis. Cells interact with eachother and diffuse, biased by extracellular chemicals, that can be altered bythe cells themselves. We use a hybrid approach where particle-based models ofcells are coupled with a PDE for the concentration of the extracellularchemical.

Particle-based simulations of reaction-diffusion processes with Aboria