Sensitivity Analysis of Quasi-Stationary Distributions (QSDs) of Mass-Action Systems

Abstract

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 an equation driven by finitely 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) besides invariant probability measures. In this paper, we modify the coupling-based technique developed in [M. Dobson, Y. Li, and J. Zhai, SIAM/ASA J. Uncertain. Quantif., 9 (2021), pp. 135–162] to estimate an upper bound of the 1-Wasserstein distance between two QSDs. Some numerical results of sensitivity with different population sizes are provided.