In the deterministic mode MesoRD will do what we call a
mean-field approximation. The approximation is that the state,
*i.e.* number of molecules, change
continuously and with the average rate given by the stochastic
description at each point in time. To see what this means,
consider the events that changes the number of A-molecules in
subvolume
during the next time period
, assuming that the systems has only one spatial dimension. The
different reactions occurs with probability
and when reaction
occurs the number of A-molecules changes by
. The A-molecules can also diffuse away with probability
to each of the two neighbouring subvolumes in one dimension. The
number of A-molecules in subvolume
can also increase if A-molecules diffuse from the neighbouring
subvolumes. They do this with probability
and
, respectively. The average change in the number of A-molecules in
subvolume
during
is therefore

where the values in parenthesis are the stoichiometries for
changes of the number of A-molecules of the different
events. Similar expressions simultaneously govern the A-molecules
in other subvolumes and other species.

If we divide Equation 6.4 by we get a system of ordinary differential equations, for instance for

where
. In the deterministic mode MesoRD solve this kind of ODE systems
numerically.

If we divide Equation 6.5 by and take the limit we get a more familiar expression for the reactions diffusion equation

with
as the continuous spatial coordinate.