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This paper studies the sensitivity analysis of mass-action systems againsttheir diffusion approximations, particularly the dependence on populationsizes. As a continuous time Markov chain, a mass-action system can be describedby a equation driven by finite many Poisson processes, which has a diffusionapproximation that can be pathwisely matched. The magnitude of noise inmass-action systems is proportional to the square root of the moleculecount/population, which makes a large class of mass-action systems havequasi-stationary distributions (QSDs) instead of invariant probabilitymeasures. In this paper we modify the coupling based technique developed in [8]to estimate an upper bound of the 1-Wasserstein distance between two QSDs. Somenumerical results for sensitivity with different population sizes are provided.

Sensitivity analysis of quasi-stationary-distributions (QSDs)