Stochastic Simulation on a Minimal Model of Cancer Immunoediting Theory

Abstract

In this paper, we explore the interplay between tumor cells and the human immune system, based on a deterministic mathematical model of minimal interactions by transforming it to stochastic model using a continuous-time Markov chain, where time is continuous but the state space is discrete. Furthermore, we simulate the stochastic basin of attraction to verify the behavior of the three critical points of interest in the deterministic system. Moreover, the stochastic simulations exemplify the cancer immunoediting theory in its three phases of development: elimination, equilibrium and escape. We extend the minimum model proposed in [DeLisi & Rescigno, 1977] to include a term of immunotherapy by lymphocyte injection, and we simulate two treatment regimes, equilibrium and escape, under several schemes.