Dynamics of tumor interaction with the host immune system (Q1334747)

The author develops a reaction-diffusion model for the initial growth of a tumor following a mutation that affects the biochemical control mechanisms of cell division. He derives a necessary and sufficient condition for the existence of travelling wave solutions. The results suggest, biologically, that for certain types of mutation growing tumors can initially contain a significant portion of normal cells. Moreover, the model predicts that there is a critical level of immune response, above which the immune system will prevent the initial growth of the tumor.