Cancer self remission and tumor stability-- a stochastic approach.

The paper aims to express the spontaneous regression and progression of a malignant tumor system as a prey--predator like system. The model is a three dimensional deterministic system, consisting of tumor cells, hunting predator cells and resting predator cells. Local stability analysis is performed along with numerical simulations to support the analytical findings. Moreover, the deterministic model is extended to a stochastic one allowing random fluctuations around the positive interior equilibrium. The stochastic stability properties of the model are investigated both analytically and numerically. The thresholds obtained from our study may be helpful to control the malignant tumor growth.