Positive and negative role of random perturbations in the dynamics of a tumor-immune system with treatment

The paper aims to study the constructive role of noise in tumor dynamics. Mathematical investigation of this problem is carried out on the basis of a model of dynamic interaction between effector and tumor cells under conditions of chemotherapy. For the deterministic variant of the model, zones of mono-, bi-, and tristability are defined depending on the bifurcation parameter of treatment intensity. We find equilibrium and oscillatory attractors associated with active, dormant and zero tumor states. The paper studies how, depending on the chemotherapy intensity, random disturbances transform the active tumor mode into the dormant, or even zero state providing the main target of treatment. We also find conditions generating stochastic transitions of the tumor-immune system from the dormant tumor to the regime of active tumor. In the mathematical study of the positive and negative role of random noise, along with direct numerical simulation and statistical processing, we use the analytical confidence domain method.