Many problems in bioscience for which observations are reported in the literature can be modelled by suitable functional differential equations incorporating a delay, parameterized by parameters p₁, p₂, ..., p_L. Given such observations (which usually contain error or `noise'), we may determine the parameters {p_i} by fitting the model equations to the data and optimizing a measure of best fit.

We describe a (new) method to estimate (i) the sensitivity of the state variables to the parameter estimates {p_i}, (ii) the sensitivity of the parameter estimates to the observations and (iii) the nonlinearity effects for delay differential models. The sensitivity of parameter estimates to the observations is low if the sensitivity of the state variables to the parameter estimates is high. Sensitivity coefficients are used to determine the covariance matrix of parameter estimates and hence to determine the standard deviations. Numerical results are used to illustrate the results.

Keywords: Sensitivity analysis, parameter estimates, neutral delay differential equation, time-lag, nonlinearity effect.

The work was prepared in collaboration with Christopher T.H. Baker.

MINISIMPOSIUM SESSION: 3. Numerical methods for delay equations (2 sessions)