Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions

Abstract

In this paper, we investigate deterministic and stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions. For the deterministic case, stability analysis is performed by Routh–Hurwitz criteria. Chaos is observed in bifurcation analysis and examined by the method of 0−1 test. The stochastic system is constructed by incorporating multiplicative white noise terms into the deterministic system. We establish a unique positive solution ensuring the positiveness and boundedness of solution from the positive initial condition. The sufficient condition is obtained for weak persistence in mean. We also derive the parametric restrictions for stochastic permanence and global attractivity in mean. Finally, we validate the extinction of tumor cells with the transition from co-existence domain by crossing the estimated threshold values of intensity of environmental noise.