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

This paper deals with the qualitative analysis of the behavior of a kinetic model, proposed in [1], 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 details. The first model deals with the tumor growth generated by the interactions between the tumor cells and those of a carcenogenic 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.