Stability Study Of Several Types Of Infectious Disease Kinetic Models

At present,infectious diseases have seriously threatened human health and safety of life and property.People pay more and more attention to the prevention and control of infectious diseases,and infectious diseases have become the public health problems at domestic and abroad,Therefore,it is a meaningful research topic to study the transmission mechanism and control strategy of infectious diseases from the view of point of dynamical model.The contents of this paper are as follows:(1)We establish a virus infection virus model with cellular immune response from the perspective of cytotoxic infection in host,(2)We formulate age structured SVIR model with vaccination,the equilibria,basic re-generation numbers,the asymptotic smoothness of the semi-flow,the existence and the persistence of the global attractor are addressed.The stability of the equilibria is proved by analyzing the characteristic equation and constructing the Lyapunov function.Finally,we perform numerical simulation to verify our conclusion to discuss the combined effects of susceptibility age,vaccination age and recurrence age on basic regeneration number.(3)We further investigate a class of hepatitis B virus infection model with spatial diffu-sion.We prove that the positive invariance of the model.The local asymptotic stability is studied by linearization method.By constructing the appropriate Lyapunov functional and LaSalle invariant principle,we prove the global asymptotic stability of the equilibria.By analyzing the dynamic properties of the model and constructing the Lyapunov functional of the equilibrium state of different models,the Lyapunov functional construc-tion method is applied to the mathematical model of infinite distribution delay,age struc-ture and reaction diffusion.The results of the global stability of the equilibrium state also provide theoretical guidance for clinical research and control strategies.