On Stability of Stochastic Delay Model for Tumor - Immune Interaction

Abstract

In this paper we study a stochastic model for tumor-immune interaction with delay. More precisely, we extend the deterministic delay tumor - immune interaction model by introducing random perturbations and obtain stochastic model. For this model, we first prove existence and uniqueness of the global positive solution, and then, by using suitable Lyapunov functionals, we obtain stability conditions for the equilibrium state when tumor cells and resting cells approach their carrying capacities. We also carry numerical simulation with reliable data to illustrate our theoretical findings.