NUMERICAL TREATMENT OF THE PARAMETER-IDENTIFICATION PROBLEM FOR DELAY-DIFFERENTIAL SYSTEMS ARISING IN IMMUNE-RESPONSE MODELING

We present an approach in this paper to the solution of parameter iden tification problem arising in immune response modelling. The models ar e formulated as stiff systems of nonlinear delay-differential equation s (DDEs). The criteria for the best-fit solution are discussed, which are appropriate when the data to be fitted varies considerably in magn itude. 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 identifi cation is based on subdivision of the total fitting interval in order to reduce the complexity of an optimization problem. Poor initial esti mates for some parameters are improved by short-cut procedures via adj usting the model with spline functions approximating the data on the w hole observation time interval. The stiff DDEs are solved by a modific ation of the DIFSUB code. An example of the real-life parameter identi fication problem for the antiviral immune response model in the contex t of the modelling of hepatitis B virus infection is presented.