SDE Model Of Virus-infected Target Cells In Recurrent Immune Disease

Immune diseases,such as AIDS,rheumatoid arthritis,etc.,often recur,with complicated classifications and different performances.The majority of patients suffer from misdiagnosis and extended diagnosis.Therefore,more and more researchers are involved in the research of this kind of disease.From a mathematical point of view,there are many researches on the ODE model of immune diseases,but it is convenient to analyze the overall development trend of the disease,and lack of analysis of the local dynamics.In this paper,an SDE model for virus-infected target cells is established for research and analysis.For the two-dimensional ODE model of virus-infected target cells,we constructed an SDE model using the Ito formula.The model has fewer parameters,which makes it easier to analyze its dynamic behavior,and numerical simulation experiments also conform to the characteristics of this type of disease.This article contains three research contents:(1)Construct the ?Ito stochastic differential equation model;(2)The relationship between each control parameter A,C,D and bifurcation parameter B in the ODE model and the infected cell Y is studied and analyzed;(3)Comparative analysis of the dynamic behavior of ODE and SDE models.First fix the two parameters of the control parameter A,C and D,then fix the other parameter,and finally observe the numerical results of the ODE and SDE models by changing the value of the bifurcation parameter B.The first chapter of this article is an introduction,mainly introducing the research background and the models related to this paper.Chapter 2 introduces the two-dimensional ODE model.Chapter 3 discusses the construction of SDE equations on the two-dimensional ODE model.Chapter 4 mainly conducts numerical simulation on ODE and SDE models,and compares and analyzes the results.Finally,a summary of the full text.