Study On Dynamic Behavior Of Tumor Model With Multi-Intervention Synergetic Mechanism Under Noise Interference

In this dissertation,aiming at the multi-intervention synergetic tumor treatment scheme,different types of stochastic differential model are developed by introducing three kinds of noise disturbances to consider the random interference factors in tumor treatment.Based on the theory of stochastic dynamics and the research method of stochastic system,the extinction,persistence and ergodic stationary distribution of the system,as well as the influences of multiple random interference factors are studied.It mainly includes the following four parts:In the first part,in view of the multi-intervention treatment cooperating chemotherapy and immunotherapy,the pulse effect of drug concentration change during treatment is characterized by impulsive differential equation.Then concerning the continuous small random interference of white noise in tumor microenvironment,an impulsive stochastic differential model is established by introducing Brownian motion.Through Ito formula,comparison theorem of impulse differential equation and some analysis techniques of inequality,in addition to the existence and uniqueness of the global positive solution,the boundedness of the expectation of the solution is proved.Moreover,the extinction and persistence of tumor cells are analyzed by applying the strong law of large numbers and other stochastic system theory.The conclusions show that random interference can inhibit the growth of tumor cells,and that synergy of chemotherapy and immunotherapy can reduce the side effects on healthy cells.In the second part,focusing on the prostate cancer(PCa)treatment strategy combining androgen deprivation therapy with dendritic cell vaccine,for the transient increase of dendritic cells after vaccination and the random interference of white noise on the tumor microenvironment,a multi-intervention synergistic pulse stochastic system is built.By selecting appropriate Lyapunov functions,then employing comparison theorem of stochastic differential equation,analysis skills of inequality and property of It? integral,not only the existence,uniqueness and the stochastic ultimate boundedness of the global positive solution,but also the threshold conditions for the extinction and persistence of PCa cells are analyzed.The results demonstrate that shortening the vaccination period is helpful to eliminate drug-resistant PCa cells and improve the survival rate of patients receiving androgen deprivation therapy.In the third part,on account of the change of microenvironment state induced by tumor treatment,an impulsive stochastic differential system with state switching is set up by introducing a continuous-time Markov chain.By utilizing appropriate Lyapunov functions,It? formula,ergodicity theory of Markov chain and analysis method of inequality,the extinction and persistence of PCa cells,and the existence of ergodic stationary distribution of system are studied.It is asserted that the dynamic behavior of PCa cells will change due to the state switching of the system,and that the PCa can be well controlled if the system state can stay in the environment with high-intensity white noise for a long time.In the fourth part,for the phenomenon that the number of tumor cells changes greatly in a short time caused by PCa cell mutation,Levy jump noise is introduced into deterministic PCa model to develop a stochastic differential model driven by Levy noise.Through appropriate Lyapunov functions and the solution formula of Levy jump stochastic differential equation,the existence and uniqueness of the global positive solution of the model are proved.Furthermore,by employing the Lévy-It?formula,the comparison theorem of Levy jump stochastic differential equation,as well as exponential martingale inequality and Borel-Cantelli lemma,the sufficient conditions for the extinction,non-persistence in the mean,weak persistence in the mean and stochastic permanence of PCa cells are obtained.