Optimal Design Techniques for Parameter Estimation in a Bacterial Growth Model

Abstract

Mathematical models are fundamental tools to analize and predict the behaviour of dynamical processes arising in different disciplines. To ensure a reliable numerically simulated data we need to choose a model that reflects the dynamics together with a suitable set of parameter values. In this work we focus on experimental design techniques for the parameter estimation of the Baranyi bacterial growth model. We present a new criterion for selecting data leading to an accurate estimation of parameters based on the incremental generalized sensitivity functions. We conduct several numerical experiments to compare the performance when data is uniformly distributed along time with classical optimal design methods and the new technique. For each data selection we perform the parameter estimation, calculate relative errors and compute confidence intervals. We show some typical results. The numerical experiments indicate that the new criterion can be used to obtain a good estimation with few measurements.