An stochastic model for the evolution of cancer cells

Starting from a nonlinear model developed in Ref. [2], the reproduction of cancer cells and lymphocytes as an stochastic phenomenon is studied. Considering the problem as a one step Markov process, a master equation (ME) is obtained, besides, the transition probabilities for two type of cells are built. An heuristic approximation of the ME as a diffusion process is presented, and after that, the rigorous omega-expansion is developed, so that the problem is separated in a macroscopic part with zero noise and other with linear noise to study the statistical moments of the fluctuations. Recurring to a numerical inspection, it is found that sudden changes could happen going from one basin to other in the space of states, with drastic modifications in the future evolution of the illness.