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Qualitative analysis of a nonlinear integrodifferential equation modeling tumor-host dynamics. (English) Zbl 0859.92011
Summary: 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
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