Mathematical Study Of The Inhibitory Role Of Regulatory T Cells In Tumor Immune Response

Tumor immune response is a complex dynamical process.In the interaction of tumor and the immune system,immune system plays a dual role,on the one hand,the immune system can activate some immune cells to kill tumor cells,such as helper T cells,effector cells and so on,but on the other hand,there are also tumor immune inhibitory reactions to help tumor escape,such as regulatory T cells(Tregs).Based on Tregs mediated tumor immune escape mechanism,we develop several tumor immune system interaction models.This thesis contains four chapters,mainly studying the effect of Tregs on tumor cell growth and the role of immunotherapy on tumor immune system.The results can help understand the role of Tregs in the tumor immune escape,and provide scientific basis and theoretical support for immunotherapy.In Chapter 1,we briefly introduce the background of tumor immune system and the role of Tregs mediated tumor immune escape,the research status of tumor growth model and tumor immune system interaction models,and the basic concepts and theories of ordinary differential equations(ODEs).In Chapter 2,we construct and study a mathematical model based on Tregs mediated tumor immune escape mechanism.We divide immune cells into three cat-egories:helper T cells,effector cells and Tregs,and build a four-dimensional ODEs model to study the dynamical properties of interaction between immune cells and tumor cells.Furthermore,we discuss the existence and stability of tumor free equi-librium and tumor presence equilibrium.By performing numerical simulations,we investigate some important parameters,such as,the stimulation rate of helper T cells by tumor cells and the inhibition rate of effector cells by Tregs,and study their effects on the dynamical properties of the model.In Chapter 3,we establish tumor treatment models,and we consider three im-munotherapies:adoptive T cell therapy,monoclonal antibody therapy and combina-tion therapy,to discuss the effects of these three treatments on tumor growth control.In Chapter 4,we summarize the research results of this thesis and give the future research problem.