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Dynamics Analysis of an SIS Epidemic Model with the Effects of Awareness
  
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KeyWord:Awareness spreading; Epidemic model; Cooperative system; Sta-bility
Author NameAffiliation
Yanan Sun Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China 
Yakui Xue Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China 
Boli Xie Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China 
Song Sun Department of Civil Engineering, Hebei University of Architecture, Zhangji-akou, Hebei 075000, China 
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Abstract:
      In this paper, an SIS model incorporating the effects of awareness spreading on epidemic is analyzed. Four kinds of equilibria of the model are given, and a new method is used to prove the stability of the equilibria. The threshold of awareness is $R_{1}^{a}$, which measures whether awareness spreads. When awareness does not spread, the basic reproduction number of disease is $R_{1}^{d}$, it is $R_{2}^{d}$ when awareness spreads. The relationship among the three kinds of thresholds is discussed in details. Specially, the effects of various awareness parameters on epidemic are analyzed. Our theoretical results suggest that raising awareness can effectively reduce the basic reproduction number of disease and reduce the spread of disease. Furthermore, numerical simulations are performed to illustrate our results.