Thermostatted kinetic theory approach to the competition between cancer and immune system cells in an inhomogeneous system

The competition between a cancer and the immune system are modelled at cell scale in the framework of thermostatted kinetic theory. Cell activation and learning are reproduced by the increase of cell activity during interactions. The fluctuations of system activity are controlled by a thermostat which reproduces the regulation of the learning process and memory loss through cell death. An algorithm, including spatial description and inspired from the direct simulation Monte Carlo (DSMC) method, is used to simulate stochastic trajectories for cell numbers and activities. We focus on the decisive role played by the thermostat. For inefficient thermalization, the divergence of the number of cancer cells is obtained in spite of favored production of immune system cells. Conversely, when the activity fluctuations are controlled, the development of cancer is contained even for weakened immune defenses. These results may be correlated to unexpected clinical observations in the case of different cancers, such as carcinoma, lymphoma, and melanoma.