A mathematical model of cell-mediated immune response to tumor.

Mathematical models of tumor-immune interactions provide an analytic framework for studying tumor-immune dynamics. In this paper, we present a mathematical model to describe tumor-immune cell interactions, focusing on the role of the natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs) in immune surveillance. According to the experimental and clinical results, we determine part of the model parameters to reduce the model parameter space. Then we analyze the local geometric properties of the equilibria of model and carry out numerical simulations to verify the conditions for the stability properties of equilibrium points. Numerical results suggest that the host immune system alone is not fully effective against progression of tumor cells, and CTLs play a crucial role in immune surveillance.