Global stability and bifurcation analysis for a class of infectious disease models withvaccination

This paper analyzes a class of SEIR model for novel coronavirus with vaccination and discusses the parameter conditions for the existence of boundary and internal equilibrium of the system. Then, we give the local stability by calculating the basic reproduction number and further investigate the global stability by constructing Lyapunov function and variational matrix. When the basic reproduction number is smaller than 1, the system is local and globally asymptotically stable at the boundary equilibrium point; When the basic regeneration number is bigger than 1, the boundary equilibrium becomes unstable and the internal equilibrium is locally and globally asymptotically stable. Using Sotomayor theorem, it is proved that trans-critical bifurcation occurs the basic regeneration number crosses 1 near the boundary equilibrium. Finally, the stability of the system is demonstrated by numerical simulation, and the epidemic situation guidance suggestions are provided in combination with the actual biological mathematical significance.