Mathematical models of therapeutical actions related to tumour and immune system competition

This paper deals with the qualitative analysis of a model related to the description of two medical therapies which have been intensively developed in recent years. In particular, we refer to the modelling of the actions applied by proteins, to activate the immune defense, and to the control of angiogenesis, to contrast the growth of tumour cells by preventing the feeding actions of endothelial cells. The therapeutical actions which are object of the modelling process developed in this paper have to be regarded as applied within the framework of the competition between the immune system and tumour cells. We prove the existence of solutions to the Cauchy problem related to the model. The efficiency of the therapies and the asymptotic behaviour in time of our solutions is also investigated.