An alternative interpretation is to consider the model as a stochastic process. In this case the reaction kinetics
are not considered to describe the rates of change for the concentrations of involved species, but rather as a
specification about the probability that a reaction event happens. If a reaction event happens the particle numbers
of the involved species are updated according to their stoichiometries. That means particle numbers are always
integer numbers and change discretely.
Specifically the value of the kinetic function is interpreted as a so called propensity, that is a differential
probability density that a reaction event will happen in the next infinitesimal time interval. However there are
subtle differences between reaction rates and reaction propensities. One of those differences that only matters for
rather small particle numbers is that e.g. the rate of a second order mass action reaction is described as
$k \left(\frac{S}{V}\right)^{2}$, while the propensity of the
same reaction is $k \, \frac{S}{V} \, \frac{S-1}{V}$. COPASI will apply this kind
of corrections automatically. In cases where these corrections have already been done by the modeler explicitly
COPASI needs to be told not to apply this correction. This is described in the
general model
settings.
Another issue modelers should be aware of is that the rate laws for enzymatic reactions that are derived using the
steady state approximation are not necessarily valid for stochastic simulation. In many cases they are, but the
underlying assumptions for using them are not exactly the same as for deterministic simulations.
