Confidence interval superiority of the two-timescale approach over the single timescale in inverse problems of parameter estimation
The multi-scale nature innate to biological systems concerns not only the space but also the time domain. Some dynamical systems, described either as an ODE or PDE system, are characterized by more than one timescale. On the paradigmatic example of an in vivo model of drug-induced enzyme production (an in vivo model of xenobiotic metabolizing enzyme induction containing 8 reactions, 6 state variables and 12 parameters), we show how the slow-fast decomposition and the first order averaging method serve for an enhanced parameter estimation when the slowly changing features are rigorously incorporated. Comparing numerical results between the one-timescale and two-timescale method, it is shown that confidence intervals for some estimated parameters are reduced for the latter. The proof supporting this superiority of the two-timescale approach over the single timescale in inverse problems of parameter estimation, for a general multiple timescale system, is under study.