Mathematical Model Of Tumor With Immune Response And Drug Therapy

Cancer is one of the most serious diseases threatening human life and health.Due to the complexity of the body,compared with other single diseases,the oc-currence and development mechanism of tumors is extremely complex.More and more evidences show that the immune system can identify and eliminate malignant tumors,one of the complexities of the immune response is that there are many types of immune cells,each of which plays a unique role in targeting and killing tumor cells.This paper is divided into four parts,which mainly studies the role of the natural killer cells and CD8+ cytotoxic T lymphocytes in immune surveillance,and tumor-immune responses to chemotherapeutic agents.Providing possible treatment direction and strong theoretical support for cancer treatment.In chapter 1,the tumor growth model,the tumor-immune system interaction model and the mathematical model of tumor treatment are introduced,and several common basic theories of ordinary differential equations are briefly described.In Chapter 2,we present a four-dimensional mathematical model to describe tumor-immune cell interactions,the existence and stability of the non-negative equilibrium point of the model are discussed and analyzed.And we carry out numerical sim-ulations to verify the conditions for the stability properties of equilibrium points.In Chapter 3,it is the analysis result according to the second chapter,in which five-dimensional mathematical model is proposed to analyze the effect of adding chemotherapeutic drugs,existence and stability of non-negative equilibrium point of this model are discussed and analyzed,and numerical simulation is carried out,and the simulation results are compared and analyzed.The fourth chapter briefly summarizes the main research results in this paper,and puts forward the shortcom-ings of this paper and the future work prospects.The results show that the immune system itself can not prevent the growth of tumor cells completely and effectively,and it requires human intervention,such as chemotherapy;the amount of chemotherapy drugs should be strictly controlled dur-ing chemotherapy,otherwise it may not be able to effectively cure cancer,and even accelerate the inactivation of immune cells;increasing the growth rate of natural killer cells is of great help to cancer treatment;and increasing the stimulating effect of dendritic cells on CD8+T cells can enhance the ability of the immune system.Therefore,we believe that chemotherapy combined with other treatments may re-duce the harm of drugs to the human body,accelerate the death of cancer cells and finally cure cancer.