Mathematical modeling of the development of dormant tumors and immune stimulation of their growth.

*(English. Russian original)*Zbl 0673.92003
Cybernetics 23, No. 4, 556-564 (1987); translation from Kibernetika 1987, No. 4, 96-102 (1987).

A mathematical model of tumor growth and multistage immune response of the host organism is considered in the form of a system of five nonlinear differential equations with a single delay (representing the time to appearance of cytotoxic lymphocytes). Stability of model equilibria is investigated using standard methods. Numerical simulations illustrate combinations of parameters for which asymptotic stability, limit cycles or instability may arise. The main point of the discussion is that the action of the immune system may, under certain conditions, lead paradoxically, to stimulation of tumor growth instead of its eradication.

Reviewer: M.Kimmel

##### MSC:

92C50 | Medical applications (general) |

92D25 | Population dynamics (general) |

34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |

##### Keywords:

delay differential equations; tumor dormancy; tumor growth; multistage immune response; cytotoxic lymphocytes; Stability of model equilibria; Numerical simulations; asymptotic stability; limit cycles; instability; immune system
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\textit{V. A. Kuznetsov}, Cybernetics 23, No. 4, 556--564 (1987; Zbl 0673.92003); translation from Kibernetika 1987, No. 4, 96--102 (1987)

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##### References:

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