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Construction and study of stability of an antitumoral immunity model. (English. Russian original) Zbl 1077.92035

Cybern. Syst. Anal. 40, No. 5, 778-783 (2004); translation from Kibern. Sist. Anal. 2004, No. 5, 177-182 (2004).
Summary: A simplified model of antitumor immunity is proposed. The model is based on the G. I. Marchuk immune protection model [see “Mathematical models in immunology.” 2nd ed. (Russian) (1985; Zbl 0603.92004)] and Gompertz model. Sufficient conditions of its asymptotic equilibrium stability are obtained and formulated in terms of characteristic quasipolynomial coefficients.

MSC:

92C50 Medical applications (general)
92C30 Physiology (general)
34D05 Asymptotic properties of solutions to ordinary differential equations

Citations:

Zbl 0603.92004
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References:

[3] V. P. Martsenyuk, ?Investigation of zeros of a quasipolynomial of the fourth degree in G. I. Marchuk?s model of immune protection,? Visnyk Kiev. Univ., Ser. Fiz-Mat. Nauk, No. 4, 207-215 (2002). · Zbl 1075.92514
[8] V. P. Martsenyuk, ?The problem of selection of a chemotherapy scheme from the viewpoint of control theory,? Probl. Upr. Inf., No. 2, 134-145 (2003).
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