Sensitivity analysis of quasi-stationary-distributions (QSDs)

TL;DR

This paper analyzes how the quasi-stationary distributions of mass-action systems are sensitive to changes in population sizes, using coupling techniques to estimate bounds on their differences.

Contribution

It introduces a modified coupling method to estimate upper bounds on the Wasserstein distance between QSDs in mass-action systems, accounting for population size effects.

Findings

Upper bounds on Wasserstein distance between QSDs derived

Sensitivity of QSDs to population size variations demonstrated

Numerical results illustrate the impact of population size on QSDs

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 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.