Neste trabalho, realizamos um estudo numérico para o modelo cosmológico de Friedmann partindo de conceitos Newtonianos. Originalmente, esse modelo foi construído utilizando o ferramental matemático da Relatividade Geral, que possui grande nível de complexidade e não é acessível para os estudantes dos níveis iniciais da graduação. Sendo assim, a abordagem desse modelo através de conceitos Newtonianos torna acessível a compreensão de alguns conceitos básicos da Cosmologia. Além disso, também é possível que o estudante utilize esse material como uma introdução aos estudos dos métodos numéricos e computacionais. Na descrição de um Universo expansivo, as equações diferenciais são resolvidas numericamente pelo Método de Runge-Kutta de quarta ordem. Os resultados apresentados pelos gráficos das soluções numéricas condizem com os dados observacionais, descrevendo qualitativamente as eras pelas quais o Universo passou. Como motivação para o estudante, disponibilizamos as rotinas computacionais em C, Octave e Simulink.
Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be weakened by the cancer. One type of cancer treatment is chemotherapy, which uses drugs to kill cancer cells. Clinical, experimental, and theoretical research has been developed to understand the dynamics of cancerous cells with chemotherapy treatment, as well as the interaction between tumour growth and immune system. We study a mathematical model that describes the cancer growth, immune system response, and chemotherapeutic agents. The immune system is composed of resting cells that are converted to hunting cells to combat the cancer. In this work, we consider drug sensitive and resistant cancer cells. We show that the tumour growth can be controlled not only by means of different chemotherapy protocols, but also by the immune system that attacks both sensitive and resistant cancer cells. Furthermore, for all considered protocols, we demonstrate that the time delay from resting to hunting cells plays a crucial role in the combat against cancer cells.
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