LAUSR

This paper focuses on the global stability of an epidemic model with vaccination, treatment and isolation. The basic reproduction number $${\mathcal {R}}_0$$R0 is derived. By constructing suitable Lyapunov functions, sufficient conditions for the global asymptotic stability of equilibria are obtained. Numerical simulations are performed to verify and complement the theoretical results. Furthermore, we consider the uncertainty and sensitivity analysis of the basic reproduction number $${\mathcal {R}}_0$$R0. The results show that the transmission rate, the fraction of infected receives treatment, vaccination rate, the isolation rate are crucial to prevent the spread of infectious diseases. These suggest that public health workers design the control strategies of disease should consider the influence of vaccination, treatment and isolation.