A model for tumor catastrophe in the presence of immunocompetent cells - Ortega, Horacio; Acosta, Antonio (Ciencia, 2011)
We present a model of the tumor-immune system interaction by means of a set of four coupled differential equations representing the tumor, effectors cells, inhibitory factors released by tumor and antitumor cytokines respectively. We discuss the stability of the system by usual methods (linearization and Routh-Hurwitz criterion). We find that there exist regions on a space of parameters associated to the tumor progression and regression. The structure of these regions provides an elegant description of tumor behavior, including the explanation of some current paradoxes and also of the so minted immune response dilemma. A fold catastrophe in our space of solutions appears to be the cause of such paradoxical behavior. Some recent reports seem to support our results.