Tumor-immune system interaction: Modeling the tumor-stimulated proliferation of effectors and immunotherapy

Tumoral dynamics and antitumor immunotherapies are likely to be influenced by the modalities of interaction between tumor cells and immune system effectors, and by the inter-effectors interactions. Within the framework of the theory of competing populations, we study here the influence of the proliferation response of effectors to tumor burden, and of cooperation and/or competition between immune system effectors, by means of three inter-related bi-dimensional meta-models. After studying their null-clines, we study the location and the local stability of the equilibria. Then, we investigate the existence and, in some cases, the uniqueness of stable limit cycles. The condition for the global asymptotically stable eradication under constant or slightly variable periodic immunotherapy is given. Finally, implications of strong saturation in the effectors ability to kill tumor cells are discussed.