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Stationarity and periodicity of positive solutions to stochastic SEIR epidemic models with distributed delay

  • Author Bio: E-mail address: liuqun151608@163.com; E-mail address: shinz@nenu.edu.cn; E-mail address: tahaksag@yahoo.com; E-mail address: aalsaedi@hotmail.com
  • Daqing Jiang, E-mail: daqingjiang2010@hotmail.com, Tel.: +86 43185099589; fax: +86 43185098237

    Daqing Jiang, E-mail: daqingjiang2010@hotmail.com, Tel.: +86 43185099589; fax: +86 43185098237 
The first author was supported by NSFC of China (No: 11561069), 2016GXNSFBA380006 and KY2016YB370, the second author was supported by NSFC of China (No: 11371085) and the Fundamental Research Funds for the Central Universities (No.15CX08011A).
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  • In this paper, we consider two SEIR epidemic models with distributed delay in random environments. First of all, by constructing a suitable stochastic Lyapunov function, we obtain the existence of stationarity of the positive solution to the stochastic autonomous system. Then we establish sufficient conditions for extinction of the disease. Finally, by using Khasminskii's theory of periodic solutions, we prove that the stochastic nonautonomous epidemic model admits at least one nontrivial positive T-periodic solution under a simple condition.

    Mathematics Subject Classification: Primary:92B05, 92D30;Secondary:34E10, 60H10.

    Citation:

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