Tumor-T Cells Immune Model Dynamic Properties And Optimal Control

In order to explore the effective theoretical methods to inhibit the growth of tumor,based on the randomness of tumor growth microenvironment and the dynamics of chemotherapy combined with immune anti-tumor,the T-cells anti-tumor stochastic model,the delayed pulse model of chemotherapy combined with immune anti-tumor,and the optimal control model of chemotherapy combined with immune anti-tumor are established.Using stochastic differential equation theory,impulsive differential equation theory and optimal control theory of pharmacokinetics to study the dynamic properties of tumor immune cells.The specific research contents are as follows:Firstly,considering the influence of random disturbance on the growth?reproduction and apoptosis of tumor cells and immune cells,a stochastic tumor immune model with Gaussian white noise is established.By using Ito's formula and strong law of large numbers,we prove the existence of globally unique positive solutions and obtain sufficient conditions for the death and weak persistence of tumor cells and T cells.Through theoretical derivation and numerical simulation,it is concluded that noise intensity is one of the important factors that directly affect the state of tumor cells and effector T cells(including extinction and weak persistence).According to the theoretical prediction and numerical simulation results,some strategies to improve the microenvironment of tumor cells and T cells are proposed.Secondly,in order to explore the frequency and dose of chemotherapy drugs and immune drugs in the process of individualized chemotherapy combined with immunotherapy,the anti-tumor model of chemotherapy combined with immunotherapy is established.study the effects of time-lag and pulse factors on the dynamic behavior of the model.Take the treatment of advanced non-small cell lung cancer as an example,carboplatin and interferon are selected as chemotherapy drugs.Based on the theory of impulsive differential equation,the growth and change of tumor cells are studied when one drug is injected alone or two drugs are injected at the same time.Finally,we refer to the research results of chemotherapy combined with immune anti-tumor model,using the principle of Pontryagin maximum to reduce the number of tumors,a chemotherapy combined immune anti-tumor optimization control model is established,and the optimal control problem is discussed.The existence of solutions and the efficacy of combined treatment strategies are discussed.Combined with the existing data in the literature,numerical simulation is used to compare the changes in the number of tumor cells and immune cells under the three treatment strategies of immunization alone,chemotherapy alone,and combined chemotherapy.