COMPORTAMENTO DINAMICO DO CRESCIMENTO DE TUMORES COM A APLICAÇÃO DE QUIMIOTERAPIA

Abstract

This study proposes to analyze mathematical models that describe the dynamics of populations, namely, sets of organisms that may or may not belong to the same species but have similar behavior as relates to their dynamics. It is specially treated with models of cell populations that consider the delay time, which are described by dierential equations with delay. The analysis is realized in two mathematical with models, the rst describes the interaction of tumor cells with the immune system. It is considered that the immune system is constituted by resting cells and hunting cells, as well as, the resting cells become cells hunting but the conversion is not straightforward, requiring shaping by delayed dierential equations. The second describes a model for treatment of cancer by chemotherapy where there is metastasis of a primary to a secondary focus by tumor cells. We observe the interactions between normal and tumor cells as being competitive for the available resources, and it is thought the chemotherapy agent as a predator in normal and cancer cells. Metastasis can occur with a delay time, which leads to delayed dierential equations. Next study is a model for treating of brain tumor by chemotherapy. We propose a system of coupled dierential equations that model brain tumour with treatment by chemotherapy, which considers interactions among the glial cells, the glioma, the neurons, and the chemotherapeutic agents. We study the conditions for the glioma growth to be eliminated, and identify values of the parameters for which the inhibition of the glioma growth is obtained with a minimal loss of healthy cells.