Global Stability of the Deterministic and Stochastic SIS Epidemic Models with Vaccination
Received:May 30, 2020  Revised:September 27, 2020
Key Word: SIS epidemic model   vaccination   global stability  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.12071058).
Author NameAffiliation
Xu ZHAO School of Mathematics and Information Science, Beifang Minzu University, Ningxia 750021, P. R. China
School of Science, Dalian Minzu University, Liaoning 116600, P. R. China 
Wenshu ZHOU School of Science, Dalian Minzu University, Liaoning 116600, P. R. China 
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Abstract:
      We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma (2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.01.007
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