Modelagem matemática para o crescimento de tumores sob interferência da quimioterapia e imunoterapia

Abstract

On the world stage, cancer is the second leading cause of death in the world, accounting for 9.6 million deaths in 2018. Globally, one in six deaths is related to the disease. In Brazil, there are an estimated 704,000 new cases of cancer for the three-year period 2023-2025. This course completion work aimed to investigate tumor growth and methods of treatment, chemotherapy and immunotherapy. The mathematical modeling that describes tumor growth was performed using systems of ordinary differential equations, based on the interspecies competition model, with adaptations for tumor and normal cell populations. An analytical study was done to understand the stability and equilibrium points of the systems. After this step, the models were solved numerically via Euler’s Method implemented by Python language. The results showed the importance of starting treatments against cancer early, due to its explosive capacity for growth. The combination of chemotherapy and immunotherapy can eliminate the tumor more quickly. Finally, we emphasize the need for screening tests by the general population and more research on new treatments or even new perspectives so that you can fight this pathology more effectively.