Stability And Bifurcation Analysis For A Class Of Age-structured Tumor Immune Model

The development of mathematical models of tumor immunity has encompassed a variety of mathematical approaches.The continuous development and application of these mathematical models provide insight and strong support for the study of tumor immunology.In this thesis,age structure and time lag are taken into account in tumor immune models,and tumor immune models with age structure and time lag are developed and their kinetic behaviors are investigated.A tumor immune model with age structure is constructed by considering the age structure of tumor cells and considering the reproductive behavior of tumors as a nonlinear proliferation function based on age.By constructing the abstract Cauchy problem,sufficient conditions for the existence of tumor free stable states and tumor stable states are obtained by applying the theories of separation variables and compression mapping,and the uniqueness of the existence of the system solution is discussed.The consistent persistence of positive equilibrium states of the system under certain conditions is verified,and we verify the relevant conclusions and analyze the sensitivity of the system parameters by numerical simulation.The age structure of generated immune cells promoted by the presence of tumors is considered and the effect of time delay in generating immune cells is considered.The existence uniqueness of the solutions of the system is obtained by constructing some results of the abstract Cauchy problem,and the influence of the time delay parameter on the dynamical behavior of the system from the point of view of the eigenvalues is analyzed using the correlation method of the operator semigroup,and the threshold value of the Hopf branch generated by the equilibrium state of the system tumor is obtained.The corresponding conclusions are verified by numerical simulations.