Study On The Bistability Of Two Kinds Of Models In The Biomedicine

The study of tumor and virus from the point of view of dynamics is a hot topic in the field of biomathematics,which is the intersection of mathematics and biology and medicine.By establishing a suitable mathematics model and analyzing the dynamics of the model effectively,can find the control threshold of related disease,which is beneficial to prevention and control of tumor and virus related disease.This paper mainly studies tumor-immune-help T cells model and virus infection model with monotonic and nonmonotonic immune response.It can be divided into the following two parts.Tumor-immune-help T cells model.Firstly,through the analysis of the existence and stability of the equilibria,it is found that the presence of help T cells can inhibit the bistable behavior in the tumor-immune model and also inhibit the occurrence of tumor high steady state.Secondly,immune intensity is used as bifurcation parameter to prove that saddle-node bifurcation and Hopf bifurcation occur.Finally,the results of numerical simulation verify the results of theoretical analysis.Virus infection model with monotonic and non monotonic immune response.In this paper,two-dimensional,three-dimensional immune response virus infection models are considered.Firstly,the appropriate threshold is selected to prove that the system with monotonic immune response has no bistability behavior and the model with nonmonotonic immune response has bistability behavior.At the same time,the global stability of the equilibria between monotonic and nonmonotonic immune response models is analyzed.Finally,the saddle-node bifurcation for nonmonotonic immune response model is analyzed.The results of numerical simulation verify the results of theoretical analysis.