Adjoint Sensitivity Analysis of Neutral Delay Differential Models

Sensitivity analysis is crucial both in the modeling phase and in the interpretation of model predictions. It contributes to model development, model calibration, model validation, reliability and robustness analysis, decision-making under uncertainty, and model reduction. Sensitivity analysis is concerned with the study of the relationship between infinitesimal changes in the model parameters and changes in model output. As an example, biological and physical problems are often subject to disturbance or perturbations in the system data. It is quite usual for a model to display very high sensitivity to small variations in some parameters, while displaying robustness to variations in other parameters; See [7, 8, 9, 10, 11, 12]. A retarded functional differential equation (RFDE) describes a system where the rate of change of state is determined by the present and the past states of the system. If the rate of change of the state depends on its own values as well, the system is called a neutral functional differential equations (NFDEs). When only discrete values of the past have influence on the present rate of change of state, the corresponding mathematical model is either delay differential equation (DDE) or neutral differential equation (NDDE). The theory of RFDEs is of both theoretical and practical interest, as they provide a powerful model of many phenomena in applied sciences such as physics, biology, economics, control theory and so on. The work reported in [1, 2, 3, 4, 5, 11, 13, 14]