An approach for benchmarking the numerical solutions of stochastic compartmental models

TL;DR

This paper introduces a benchmarking method for stochastic compartmental models by comparing their simulated distributions with analytical ODE solutions, enabling validation of numerical solutions across different biological models.

Contribution

The work presents a novel approach for verifying stochastic model simulations against analytical solutions without requiring specific model states or limits.

Findings

Feasibility of checking stochastic model adherence to ODEs.

Applicable to various models like SIR and Lotka-Volterra.

Provides a basis for unit testing and validation of stochastic simulations.

Abstract

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.