Modeling the dynamics of glioma-immune surveillance

The proposed mathematical model describes how glioma cells evolve and survive the brief encounter with the immune system mediated by macrophages and the tumor specific CD8+T cells. We characterize the dynamics of the system by observing biologically realistic singular points and their stability analysis. The global asymptotic stability of the interior equilibrium point is studied with the help of Lyapunov method and we prove the uniform persistence by using the method of average Lyapunov function. The numerical simulation demonstrates that the model, with the parameter assumptions and values we used, is capable of reproducing glioma escape from immune surveillance in a biologically realistic time frame. We investigate the conditions under which the macrophages can be infiltrated, and identify the parameter values for which the inhibition of the gliomas proliferation is acquired.