Tumors under periodic therapy -- Role of the immune response time delay

We model the interaction between the immune system and tumor cells including a time delay to simulate the time needed by the latter to develop a chemical and cell mediated response to the presence of the tumor. The results are compared with those of a previous paper, concluding that the delay introduces new instabilities in the system leading to an uncontrolable growth of the tumour. Then a cytokine based periodic immunotherapy treatment is included in the model and the effects of its dossage are studied for the case of a weak immune system and a growing tumour. We find the existence of metastable states (that may last for tens of years) induced by the treatment, and also of potentially adverse effects of the dossage frequency on the stabilization of the tumour. These two effects depend on the delay, the cytokine dose burden and other parameters considered in the model.