Stability Analysis Of A Hepatitis B Age Structure Epidemiological Model With Vaccination

In this paper,we formulated an age-dependent model for the transmission dynamics of HBV with vaccination.Considering acute infectious individuals and carriers have age-structure that we construct a class of combined biomechanical model with ordinary differential equations and partial differential equations.We get the following results through the study of model dynamics:Basic reproduc-tion number R0 determines the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium.If R0? 1,the disease-free equilibrium is globally asymp-totically stable,If R0>1,then the unique endemic equilibrium is globally asymptotically stable.Since the model is a kind of mixed infinity dimensional dynamical system that we prove the asymptotic smoothness of the solutions and the uniform persistence of the sys-tem,then we get the existence of the global attractor.The global stability of the balance state is obtained by constructing the Lyapunov function on the global attractor.Biologically,the result obtained by numerical simulation is that vaccination is a good way to control the disease.The disease will disappear by using appropriate vaccination strategies.Increasing infection probability from infectious individuals to the carriers is also an effective way to control disease.Further more,we find that the more number of infected individuals develop into carriers,the more likely to eradicate disease through the vaccination strategy.