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Behaviour of solutions to Marchuk’s model depending on a time delay. (English) Zbl 0947.92015
Summary: G. I. Marchuk’s [Mathematical models in immunology (1983; Zbl 0556.92006); Mathematical modelling of immune response in infectious diseases. (1997; Zbl 0876.92015)] model of an immune reaction is a system of differential equations with a time delay. The aim of this paper is to study the behaviour of solutions to Marchuk’s model depending upon the delay of immune reaction and the history of an illness. We study Marchuk’s model without delays, with a constant delay and with an infinite delay. A continuous dependence on the delay is considered. Bifurcation points are found using computer simulations.

92C50 Medical applications (general)
34K20 Stability theory of functional-differential equations
92C30 Physiology (general)
34K25 Asymptotic theory of functional-differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics