Sensitivity analysis for multiscale stochastic reaction networks using hybrid approximations

We consider the problem of estimating parameter sensitivities for stochastic models of multiscale reaction networks. These sensitivity values are important for model analysis, and, the methods that currently exist for sensitivity estimation mostly rely on simulations of the stochastic dynamics. This is problematic because these simulations become computationally infeasible for multiscale networks due to reactions firing at several different timescales. However it is often possible to exploit the multiscale property to derive a "model reduction" and approximate the dynamics as a Piecewise Deterministic Markov process (PDMP), which is a hybrid process consisting of both discrete and continuous components. The aim of this paper is to show that such PDMP approximations can be used to accurately and efficiently estimate the parameter sensitivity for the original multiscale stochastic model. We prove the convergence of the original sensitivity to the corresponding PDMP sensitivity, in the limit where the PDMP approximation becomes exact. Moreover we establish a representation of the PDMP parameter sensitivity that separates the contributions of discrete and continuous components in the dynamics, and allows one to efficiently estimate both contributions.