Dynamical Analysis Of HBV Model With Age Structure And Control Measures

It’s been known for a long time that infectious diseases do great harm to mankind,constituting a major health and economic problem and resulting in much morbidity and mortality.With the development of science and technology,the measures of preventing and controlling the epidemic diseases have been improved greatly.Hepatitis B is a potentially life-threatening liver infection caused by the hepatitis B virus.Although there is no widely available treatment for its chronic infection,this disease can be safely and effectively prevented by vaccination,and it is expected to be more efficient in control strategy.This paper focuses on proposing mathematical models for hepatitis B infection with age structure and control measures,including birth vaccination and treatment,performing their dynamics analytically and carrying out simulations numerically as well as conducting model application.Considering the implementation of birth vaccination and treatment,a model with ordinary equations is proposed and analyzed.Using Lasalle’s invariance principle and Hurwitz criterion,the stability of the equilibrium is studied and the model application for Hepatitis B transmission in China is conducted according to the yearly new reported data.Meanwhile,the optimal control strategy of the corresponding optimality system is performed by Pontryagin Maximum Principle,with the objective function of minimizing the number of susceptible and infected individuals as well as the cost.The comparison of different consequences when the optimal control or current intervention is implemented respectively,with the aim to reveal the effectiveness of optimal control measures.Based on the above ODE model,an age-structure model is formulated to study the possible effects of age on hepatitis B transmission dynamics.The stability of equilibria and persistence of the model are analyzed,which shows that its dynamic behavior is completely determined by the basic reproduction number.If R0<1 then the disease-free equilibrium is globally asymptotically stable.If R0>1,there exists a unique endemic equilibrium which is locally asymptotically stable,and the disease is uniformly persistent.Numerical simulations illustrate the different effects of variable infectivity on the disease transmission,which shows the necessity of incorporating age structure in hepatitis B modeling.Due to the fact of population migration at regional,national and global scales,we investigate the effect of immigration on HBV transmission dynamics,based on the above age-structured model.For this model,there exists no disease-free equilibrium or reproduction number.We show that the unique endemic equilibrium exists only when immigration into the infective class is measurable.Global stability of the unique endemic equilibrium is shown by a Lyapunov functional for a special case.