Abstract
This paper considers an SEIQS model with nonlinear incidence rate. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficent conditions for the global stability of the endemic equilibrium by the compound matrix theory. In addition, we also study the phenomena of limit cycle of the systems with the numerical simulations.
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