Threshold dynamics of a time periodic and two–group epidemic model with distributed delay

  • Received: 14 May 2016 Accepted: 31 December 2016 Published: 01 October 2017
  • MSC : Primary: 35K57; Secondary: 35B10, 35B35, 34B40, 92D30

  • In this paper, a time periodic and two–group reaction–diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number $R_0$ for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of $R_0$, that is, the disease is uniformly persistent if $R_0 \gt 1$, while the disease goes to extinction if $R_0 \lt 1$. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio–temporal variables.

    Citation: Lin Zhao, Zhi-Cheng Wang, Liang Zhang. Threshold dynamics of a time periodic and two–group epidemic model with distributed delay[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1535-1563. doi: 10.3934/mbe.2017080

    Related Papers:

  • In this paper, a time periodic and two–group reaction–diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number $R_0$ for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of $R_0$, that is, the disease is uniformly persistent if $R_0 \gt 1$, while the disease goes to extinction if $R_0 \lt 1$. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio–temporal variables.
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