Study On The Dynamic Properties Of Several Tumor Immune Response Systems

At present,many kinds of tumor diseases are more and more harmful to human beings.According to the analysis of relevant agencies,it is predicted that by 2030,tumor will surpass cardiovascular disease and become the biggest threat to human life.Therefore,the research on tumor is more important and urgent.In this paper,the two-dimensional model of tumor immune response proposed by stepanova in 1980 is used to analyze the dynamic behavior of the model.According to the limitation of the growth of tumor cells in vivo,the model was modified,and a tumor immune response system with time-delay effect was proposed.The main contents of the study are as follows:System 1:the hypothesis is a tumor immune response system with exponential growth of tumor cells without the effect of immune cells.In addition,the stability of the equilibrium point with a single delay and the existence of Hopf bifurcation are considered.When the time lag is not considered,we can get from the changes of the relationship between parameters,the tumor equilibrium point corresponding to the development of tumor depends on the initial state,according to which the feasible region of the model is divided into tumor free region,tumor area and cancer area,and the final trend of tumor is predicted by changing the parameter value.System 2:the hypothesis is that the growth of tumor cells follows the logistic law when there is no immune cell.After the system is dimensionless,firstly,the nonnegativity and boundedness of the solution are analyzed.Secondly,the existence of the system equilibrium point is discussed in detail.The discussion method is to transform the existence of the positive equilibrium point into the existence of the root of the univariate cubic function with the number of tumor cells as the argument.Finally,the stability of the equilibrium points without considering the time delay is analyzed,and the stability of the equilibrium point with single time delay effect and the existence of Hopf bifurcation are discussed.On the basis of theoretical derivation of two kinds of tumor immune response system,according to the results of theoretical derivation,the parameters involved in the system are selected reasonably,and the image simulation of the parameters is carried out by using the analysis software MATLAB,so as to verify the correctness of theoretical analysis and make the results more intuitive.