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.

翻译：本文提出了一种方法，用于比较传染病或生物过程中随机房室模型的估计状态与相应常微分方程组（ODEs）的解析解。采用Reed-Frost链式二项分布或Gillespie算法，在离散时间区间内数值生成随机模型的正整数样本，并将模拟实现的分布与ODEs模型解析获得的精确解进行对比。通过这种新方法，本研究证明了验证随机房室模型的实现是否符合其所代表的ODEs模型是可行的，且不要求模型处于任何特定状态或极限。这些技术基于易感-感染-恢复（SIR）传染病过程的随机房室模型开发，随后以Lotka-Volterra模型为例，说明所提出原理的普适性。该方法提供了一种测试/基准化随机房室模型数值解的途径（例如通过单元测试），以检查计算机代码及其对应算法是否符合底层ODEs模型。