Mathematical analysis of the generalised model of chemotherapy of low grade gliomas

We discuss mathematical properties of a generalisation of a model formulated in Bogdańska et al., Math Biosci (2017) that describes evolution of a type of brain tumours, namely low grade gliomas. The proposed model, consisting of ordinary differential equations, reflects the basic phenomena concerning the growth and response to chemotherapy of these tumours. Here we study the long-therm behaviour of the model solutions, when the chemotherapy is described by asymptotically periodic or constant function. The generalisation involves a general logistic term for the tumour growth and the assumption that cells affected by chemotherapy and those undamaged can have different rates of competition for resources.