Uncertainty and sensitivity analysis of biological delayed models with noise
Sprache des Vortragstitels:
Workshop on "Numerical Analysis of Multiscale Problems & Stochastic Modelling"
Sprache des Tagungstitel:
The knowledge of biological phenomena is often incomplete because
experimental measures are lacking and variances in many of the parameters values occur due to extensive variability in the data. Uncertainty and Sensitivity Analysis helps to characterise and control these uncertainties associated with a model. Uncertainty analysis (UA) quanties
the uncertainty in the outcome of a model produced by the uncertainty in
parameter inputs. Sensitivity Analysis (SA) has the complementary role
of investigating what parameters contribute most to the outcome value.
Several methods have been developed to deal with US analysis: dieren-
tial analysis, response surface methodology, Monte Carlo (MC) analysis,
and variance decomposition methods. For the purpose of this work we
are interested in the Latin hypercube sampling (LHS) method for what
concerns the uncertainty analysis and in the Partial Rank Correlation
Coecient (PRCC) and Extended Fourier amplitude test (eFAST) for
the sensitivity analysis. We implement Matlab codes to perform the un-
certainty and sensitivity analysis of stochastic models with delay. The
uncertainty in the model output generated from uncertainty in parameter
inputs is investigated. We obtain a classication of suitable thresholds of
the delays to predict the stability switch of the positive equilibrium point.
We apply our algorithm to biological stochastic model with memory terms
and compare our results with the deterministic counterparts. Finally it is
provided a discussion of biological implications. This is a joint work with Margherita Carletti (Institute of Biomath-
ematics, University of Urbino, Italy) and Gaetano Zanghirati ( Depart-
ment of Mathematics, University of Ferrara, Italy).