Sensitivity analysis based on the direct differential method for dynamical systems with discrete delays.

Mathematical models appear in many forms, such as instantaneous dynamics (ordinary differential equations) or time-lags dynamics (delay differential equations). It is important to investigate the effect on the model outputs when a perturbation is applied to the initial or boundary conditions, time delay parameters, or any model parameters in the governing equations. In this paper, we study the general theory of sensitivity analysis based on the direct differential method for systems governed by delay differential equations. Problems governed by ordinary differential equations can also be considered as a particular case of delay differential equations with the absence of delays. The normalized forward sensitivity indices are then computed to identify the important model inputs. To show the efficiency of the methodology, we apply the theory and numerical computations to immunology and infectious disease models. [ABSTRACT FROM AUTHOR]