Sensitivity Analysis of Parameters in Modelling With Delay-Difierential Equations

Many problems in bioscience for which observations are reported in the literature can be modelled by suitable functional difierential equations incorporating a delay, parameterized by parameters p1,p2,:::,pL. Given such observations (which usually contain error or ‘noise’), we may determine the parameters by optimizing a measure of best flt. It is often desirable to have information about \sensitivity" aspects of the problem. For example, the user may wish to estimate the efiect of perturbing the parameters on the solution. In data-fltting, it may be important to know the efiect of small changes of the data on the parameter estimates. In addition, one mightwishto determine the efiect ofnonlinearity ofthe model solutions. Ouraiminthispaperistoproduceanewmethodtoestimate(i)thesensitivityofthestate variablestotheparameterestimates fpig,(ii)thesensitivityoftheparameterestimatestothe observations and (iii) the nonlinearity efiects for delay difierential models. The sensitivity of the parameter estimate to the observation is low if the sensitivity of the state variable to the parameterestimateis high. Sensitivitycoe‐cientsareusedtodeterminethecovariancematrix of parameter estimates and hence to determine the standard deviations. Numerical results, basedongrowthof E.colicolonies, areusedto illustrate theresults.