  An approach is introduced for comparing the estimated states of stochastic
compartmental models for an epidemic or biological process with analytically
obtained solutions from the corresponding system of ordinary differential
equations (ODEs). Positive integer valued samples from a stochastic model are
generated numerically at discrete time intervals using either the Reed-Frost
chain Binomial or Gillespie algorithm. The simulated distribution of
realisations is compared with an exact solution obtained analytically from the
ODE model. Using this novel methodology this work demonstrates it is feasible
to check that the realisations from the stochastic compartmental model adhere
to the ODE model they represent. There is no requirement for the model to be in
any particular state or limit. These techniques are developed using the
stochastic compartmental model for a susceptible-infected-recovered (SIR)
epidemic process. The Lotka-Volterra model is then used as an example of the
generality of the principles developed here. This approach presents a way of
testing/benchmarking the numerical solutions of stochastic compartmental
models, e.g. using unit tests, to check that the computer code along with its
corresponding algorithm adheres to the underlying ODE model.
