Noise-assisted interactions of tumor and immune cells

We consider a three-state model comprising tumor cells, effector cells, and tumor-detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress tumor cell growth completely. Whereas the deterministic model does not reveal a stable tumor-free state, the auto-correlated noise combined with cross-correlation functions can either lead to tumor-dormant states, tumor progression, as well as to an elimination of tumor cells. The auto-correlation function exhibits a finite correlation time tau, while the cross-correlation functions shows a white-noise behavior. The evolution of each of the three kinds of cells leads to a multiplicative noise coupling. The model is investigated by means of a multivariate Fokker-Planck equation for small tau. The different behavior of the system is, above all, determined by the variation of the correlation time and the strength of the cross-correlation between tumor and tumor-detecting cells. The theoretical model is based on a biological background discussed in detail, and the results are tested using realistic parameters from experimental observations.