Study On The Dynamics Of Tumor Cell Interaction With Cytokines And Dendritic Cells

Two types of stochastic tumor immune systems were studied in this paper.First,the first system involved cytokines in the tumor immune system under white noise interference.The existence and uniqueness of the global positive solution is proved by random Lyapunov analysis method.At the same time,the stochastic ultimate boundedness and stochastic persistence of the system solutions are proved in turn.In addition,using the construction of auxiliary processes,the stochastic comparison theorem and strong ergodicity,we derive sufficient conditions for the extinction and persistence of tumor cells.Secondly,the second system is a stochastic tumor immune system in which tumor cells interact with dendritic cells under the interference of white noise.This system describes the interaction between dendritic cells in the blood,dendritic cells within the tumor,effector cells,and tumor cells.For this system,this article still carries on the research from four aspects.By constructing proper Lyapunov functions,the existence and uniqueness of global positive solutions,the stochastic ultimate boundedness and stochastic persistence of system solutions are proved successively.In addition,using the stochastic comparison theorem and strong ergodicity,we found that the white noise intensity of tumor cells was high,the disease would be extinct.Finally,the theoretical analysis of the above two systems is verified by numerical experiments.