Abstract: Firstly, in view of characteristics of different infectivity of hepatitis B infectors and virus carriers in the process of hepatitis B transmission, we established an S^a_kSⁿ_kV_kE_kI_kC_kR_k epidemic model with stage-structured   on complex networks.  Secondly, we obained  the basic reproduction number R₀ by using the next generation matrix method, and  combined the matrix theory and the Lyapunov function method to prove the stability of the disease equilibrium point. We also discussed the optimal control problems of two strategies  by Pontryagin’s maximum principle. Finally, based on the scale-free network, the sensitivity analysis and numerical simulation were carried out to verify the theoretical results and find the optimal control.  The results show that reducing vaccine inefficacy rate and increasing vaccination rate can better control the spread of infectious diseases.

Key words: complex network, hepatitis B virus, vaccination, optimal control