Numerical treatment of the parameter identification problem for delay-differential systems arising in immune response modelling

Abstract

We present an approach in this paper to the solution of parameter identification problem arising in immune response modelling. The models are formulated as stiff systems of nonlinear delay-differential equations (DDEs). The criteria for the best-fit solution are discussed, which are appropriate when the data to be fitted varies considerably in magnitude. The fitting procedures are based on a combination of crude but global methods of fitting the models to data and more accurate locally convergent techniques. An algorithm for sequential parameter identification is based on subdivision of the total fitting interval in order to reduce the complexity of an optimization problem. Poor initial estimates for some parameters are improved by short-cut procedures via adjusting the model with spline functions approximating the data on the whole observation time interval. The stiff DDEs are solved by a modification of the DIFSUB code. An example of the real-life parameter identification problem for the antiviral immune response model in the context of the modelling of hepatitis B virus infection is presented.