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Dynamics of the tumor – immune system competition – the effect of time delay. (English) Zbl 1035.92019
Summary: The model analyzed in this paper is based on the model set forth by V. A. Kuznetsov et al. [Bull. Math. Biol. 56, 295–321 (1994; Zbl 0789.92019)], which describes competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve a better compatibility with reality.

MSC:
92C50 Medical applications (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
Keywords:
tumor growth
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