Space-velocity thermostatted kinetic theory model of tumor growth

The competition between cancer cells and immune system in inhomogeneous conditions is described at cell scale within the framework of thermostatted kinetic theory. Cell learning reproduced by increased activity during favorable interactions. fluctuations are controlled a thermostat. direction velocity changed according to stochastic rules mimicking dense fluid. We develop Monte Carlo algorithm inspired from direct simulation (DSMC) method initially used for dilute gases. simulations generate trajectories sampling equations distributions different types. evolution an localized tumor analyzed. Qualitatively behaviors observed as field regulating decreases. For high values, i.e. efficient thermalization, controlled. small rapidly monotonously escapes immunosurveillance. critical value separating these two domains, 3E's immunotherapy reproduced, with apparent initial elimination cancer, long quasi-equilibrium period followed large fluctuations, final escape even favored production cells. values slightly smaller than value, more regular oscillations number spontaneously agreement clinical observations. antagonistic effects that stimulation may have on oncogenesis model activity-weighted rate constants autocatalytic productions Local launching met fluctuating system, able cluster larger activities those surrounding