Modelo matemático de tratamento de câncer via quimioterapia em ciclos

Abstract

The cancer is one of the leading causes of death in the world and affects a considerable portion of the population, particularly in developing countries. According to the World Health Organization (WHO, 2014), 8.2 million people worldwide died from cancer in 2012. In 2014 there are 576 000 new cases of cancer expected in Brazil (Brasil, 2014). Yet, many of these deaths could be avoided. Over 30% of canceres can be prevented by healthy life style or by immunization against cancer causing infections (HBV, HPV). Others can be detected early, treated and cured. Even in the late stage, the suffering of patients can be relieved with good palliative care. In this dissertation, we present a mathematical model with the goal of understanding tumor development and the effect of administration in cycles according two protocols of chemotherapy as well as two methods of drug delivery We begin with an introduction to the biology of cancer taking into account the main aspects for the construction of the mathematical model. Then, a review of the literature for the mathematical model is presented, and then we present a linear stability analysis for the spatially homogeneous model with and without treatment, in order to understand the dynamics of the model. We conclude that the parameters of competition are the main bifurcation parameters of the system, which define the tumor progression and the successful of chemotherapy. With these results and numerical simulations we concluded that the metronomic protocol proves more effective in prolonging the patient's life than the MTD protocol. Moreover, the uniform delivery method along with the metronomic protocol is the most efficient in reducing the density of the tumor during treatment

O câncer é uma das principais causas de morte no mundo e afeta uma parcela considerável da população, particularmente em países subdesenvolvidos. De acordo com os dados fornecidos pela Organização Mundial da Saúde (WHO, 2014), 8,2 milhões de pessoas morreram em 2012 devido ao câncer. De acordo com o Instituto Nacional do Cˆancer (Brasil, 2014), a estimativa para o ano de 2014 aponta para a ocorrência de, aproximadamente, 576 mil casos novos de câncer no Brasil. No entanto, muitas destas mortes poderiam ser evitadas. Por exemplo, mais de 30% das mortes poderia ser impedida por um estilo de vida saudável ou por imunização contra infecções que causam câncer (HPV, HBV). Ainda, cânceres detectados precocemente podem ser tratados e curados. Mesmo com câncer em estágio final, o sofrimento dos pacientes pode ser aliviado com um bom cuidado paliativo