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Numerical treatment of the parameter identification problem for delay- differential systems arising in immune response modelling. (English) Zbl 0812.65059

This paper deals with some of the practical aspects of parameter identification in systems of nonlinear delay-differential equations (DDEs), with particular reference to modelling the immune response to viral and bacterial infections.
An outline for modelling the immune response to infections by DDEs is presented in Section 2. The “best-fit” criteria and the algorithmic approaches to solving numerically the parameter identification problems in stiff nonlinear DDEs are described in Section 3.
The fitting procedures are based on a combination of global methods of fitting the models to data and more accurate locally convergent techniques. The algorithm for sequential parameter identification is based on subdivision of the total fitting interval in order to reduce the complexity of an optimization problem.
Section 4 presents a real-life application example of parameter estimation for the hepatitis B virus infection model. The example illustrates the major difficulties associated with parameter identification for immune response models.
Reviewer: G.Dimitriu (Iaşi)

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
92D30 Epidemiology
34A55 Inverse problems involving ordinary differential equations
34K05 General theory of functional-differential equations
34E13 Multiple scale methods for ordinary differential equations
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