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Zbl 1217.92076
Zhang, Zhonghua; Wu, Jianhua; Suo, Yaohong; Song, Xinyu
The domain of attraction for the endemic equilibrium of an SIRS epidemic model.
(English)
[J] Math. Comput. Simul. 81, No. 9, 1697-1706 (2011). ISSN 0378-4754

Summary: A new method is adopted to construct a Lyapunov function for the endemic equilibrium of the {\it J. Mena-Lorca} and {\it 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.
MSC 2000:
*92D30 Epidemiology
37N25 Dynamical systems in biology
34D20 Lyapunov stability of ODE
90C90 Appl. of mathematical programming
92-08 Computational methods (appl. to natural sciences)

Keywords: LMI optimization; Lyapunov function; stability

Citations: Zbl 0748.92012

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