| The production of tumor cells will cause the immune response of the body's internal immune system,and the activated autoimmune mechanism will automatically resist invading cells and eliminate foreign bodies.Various immune cells in the organism have a certain time delay(immediate delay)in the immune response of the latent tumor cells.This complex immune response process can be characterized and described by the delayed immune system.In this paper,two types of differential equation models with tumor immune delay are established,and their dynamic properties are analyzed to provide a quantitative reference for better research on tumor immune dynamics.This article is divided into three chapters.The first chapter summarizes the background of the problem,the current research status at home and abroad,and the main research content of this article.Taking into account the time delay in the process of transforming uninfected tumor cells into infected tumor cells,in Chapter 2,we established a three-dimensional differential equation model of tumor immune delay with virus infection,focusing on the analysis of time The stability of the positive equilibrium point of the model tumor in the presence of lag factors obtains the condition for the existence of Hopf branch.Numerical simulation supports the theoretical analysis results.In order to better study the complex immune response mechanism of immune cells killing tumor cells,in Chapter 3,we established a type of tumor immune delay model with Holling-? functional response function.The existence and stability of the equilibrium point in the case of time delay and time delay are discussed;the discrete time delay is used as the branch parameter to obtain the condition of the existence of the Hopf branch.The final numerical simulation showed that a periodic solution appeared near the time-positive equilibrium pointE*when???0,and the periodic oscillation of the numerical solution proved the long-term recurrence of the tumor. |
PDF Full Text Request