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We propose a novel measure valued process which models the behaviour ofchemical reaction networks in spatially heterogeneous systems. It modelsreaction dynamics between different molecular species and continuous movementof molecules in space. Reactions rates at a spatial location are proportionalto the mass of different species present locally and to a location specificchemical rate, which may be a function of the local or global species mass aswell. We obtain asymptotic limits for the process, with appropriate rescalingdepending on the abundance of different molecular types. In particular, whenthe mass of some species in the scaling limit is discrete while the mass of theothers is continuous, we obtain a new type of spatial random evolution process.This process can be shown, in some situations, to correspond to ameasure-valued piecewise deterministic Markov process in which the discretemass of the process evolves stochastically, and the continuous mass evolves ina deterministic way between consecutive jump times of the discrete part.

A spatial measure-valued model for chemical reaction networks in heterogeneous systems