An Efficient Implicit Tau-Leaping Method for Estimating Second-Order Sensitivities of Stiff Stochastic Biochemical Systems

Stochastic modelling has become increasingly important for studying biochemical systems at the cellular level. One of the most commonly used stochastic discrete models of biochemical systems is the Chemical Master Equation. Sensitivity analysis is a fundamental tool for examining how model output changes with variations in model parameters, while second-order sensitivities offer insight into parameter interactions, and provide essential information for parameter estimation and experimental design. Finite-difference approximation of second-order sensitivities can be computationally challenging, especially for stiff biochemical systems, for which reactions occur on widely different scales in time. We propose a finite-difference strategy that uses an adaptive implicit tau-leaping method to estimate second-order parametric sensitivities efficiently. Numerical experiments on several stiff models of practical interest show that the proposed method achieves accuracy comparable to existing approaches while substantially reducing the computational cost.