Classroom Note: Global Stability in an S→I→R→I Model

An S ---> I ---> R ---> I epidemic model with vital dynamics, temporary immunity, and nonlinear incidence rate is analyzed. This model consists of a system of nonlinear ordinary differential equations and can be seen as an extension of the model proposed by Tudor [SIAM Rev., 32 (1990), pp. 136--139] for herpes viral infections in which R is a latent class. Using an elementary analysis of Lienard's equation and Lyapunov's direct method, sufficient conditions are derived for the global asymptotic stability of the disease-free and endemic equilibria in this model.