  We consider molecular communication networks consisting of transmitters and
receivers distributed in a fluidic medium. In such networks, a transmitter
sends one or more signalling molecules, which are diffused over the medium, to
the receiver to realise the communication. In order to be able to engineer
synthetic molecular communication networks, mathematical models for these
networks are required. This paper proposes a new stochastic model for molecular
communication networks called reaction-diffusion master equation with exogenous
input (RDMEX). The key idea behind RDMEX is to model the transmitters as time
series of signalling molecule counts, while diffusion in the medium and
chemical reactions at the receivers are modelled as Markov processes using
master equation. An advantage of RDMEX is that it can readily be used to model
molecular communication networks with multiple transmitters and receivers. For
the case where the reaction kinetics at the receivers is linear, we show how
RDMEX can be used to determine the mean and covariance of the receiver output
signals, and derive closed-form expressions for the mean receiver output signal
of the RDMEX model. These closed-form expressions reveal that the output signal
of a receiver can be affected by the presence of other receivers. Numerical
examples are provided to demonstrate the properties of the model.

Computational Engineering, Finance, and Science;Biological Physics;Quantitative Methods