Mathematical modelling of cancer evolution

The term "cancer" refers to a group of diseases which can affect almost any tissue and organ and are characterised by the uncontrolled growth of abnormal cells, whose cell cycle is much faster than the one of a healthy cell. The carcinogenesis, i.e. the production of a cancer, is due to mutations that occur physiologically during the DNA replication process. From a mathematical point of view, many aspects can be studied. In this thesis, we focus on tumour initial developement, modelling the oncogenesis through a system of ordinary differential equations (ODEs), taking into account the possibility that a mutation occurs and the competition among healthy cells and cancer cells for the available resource, such as physical space to develop, nutrients and oxygen. The model is later analysed: it is done analitically when we are differentiating between healthy cells and cancer ones; otherwise, if we want to consider n different genotypes, the study is numerical. Some biological interpretation is given to the results