EQUAÇÕES DIFERENCIAIS APLICADAS AO CRESCIMENTO DE TUMORES

Abstract

A possible way to stop the growing of cancer cells is the chemotherapy. That is, the treatment with a drug or combination of drugs through some protocol. There are many experimental and theoretical studies about the effects of the chemotherapy on the cells.Moreover, mathematical models have been considered to simulate the growth of cancer cells, as well as, tumor-immune interactions with chemotherapy. In this thesis we investigate a mathematical model that not only take into considerations the attention of lymphocytes, but also the effect of the chemotherapy. We extend the model of Banerjee and Sarkar by adding the chemotherapy, and by considering some clinically plausible protocols. Firstly, a continuous chemotherapy is analyzed. Secondly, the traditional or pulsed chemotherapy protocol, in which the drug is administered periodically. According to experimental protocols we have used a constant amplitude for the control inputs and an oscillatory amplitude. Our main results are the cancer suppression applying continuous chemotherapy without the vanishing of the lymphocites, and pulsed chemotherapy protocols to maximize the kill of cancerous cells while minimizing the negative effects on normal cells.