Complete global analysis of an SIRS epidemic model with graded cure and incomplete recovery rates

In this paper, applying two types of Lyapunov functional techniques to an SIRS epidemic model with graded cure and incomplete recovery rates, we establish complete global dynamics of the model whose threshold parameter is the basic reproduction number R 0 such that the disease-free equilibrium is globally asymptotically stable when R 0 ⩽ 1 , and the endemic equilibrium is globally asymptotically stable when R 0 > 1 .