Qualitative analysis of a nonlinear integrodifferential equation modeling tumor-host dynamics.

*(English)*Zbl 0859.92011Summary: This paper deals with the qualitative analysis of the behavior of a kinetic model, proposed by N. Bellomo and G. Forni [ibid. 20, No. 1, 107-122 (1994; Zbl 0811.92014)], of the interactions among tumor, host environment, and immune system. It is shown that for a particular choice of the parameters of the model, the basic information is contained in the corresponding macroscopic model. The analysis is first developed for the general model. Then, two simplified models are studied in detail. The first model deals with the tumor growth generated by the interactions between the tumor cells and those of a carcinogenic environment. The second one also includes interactions between pairs of tumor cells. In both cases, conditions for blow-up/decay of the tumor are described.

##### MSC:

92C50 | Medical applications (general) |

45M05 | Asymptotics of solutions to integral equations |

34C99 | Qualitative theory for ordinary differential equations |

34E99 | Asymptotic theory for ordinary differential equations |

45K05 | Integro-partial differential equations |

45M99 | Qualitative behavior of solutions to integral equations |

##### Keywords:

tumor-immune systems; kinetic model; host environment; tumor growth; interactions; tumor cells; carcinogenic environment; blow-up/decay
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\textit{L. Arlotti} and \textit{M. Lachowicz}, Math. Comput. Modelling 23, No. 6, 11--29 (1996; Zbl 0859.92011)

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##### References:

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