Summary: A new method is adopted to construct a Lyapunov function for the endemic equilibrium of the J. Mena-Lorca
and H. W. Hethcote
[J. Math. Biol. 30, No. 7, 693–716 (1992; Zbl 0748.92012
)] SIRS epidemic model with bilinear incidence and constant recruitment. On the basis of the Lyapunov function, the domain of the attraction of the endemic equilibrium is estimated by solving a linear matrix inequality (LMI) optimization problem with multivariate polynomial objective function and constraints.