  This paper studies the sensitivity analysis of mass-action systems against
their diffusion approximations, particularly the dependence on population
sizes. As a continuous time Markov chain, a mass-action system can be described
by a equation driven by finite many Poisson processes, which has a diffusion
approximation that can be pathwisely matched. The magnitude of noise in
mass-action systems is proportional to the square root of the molecule
count/population, which makes a large class of mass-action systems have
quasi-stationary distributions (QSDs) instead of invariant probability
measures. 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. Some
numerical results for sensitivity with different population sizes are provided.
