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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 1535 - 1563, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017080

 
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Lin Zhao - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)
Zhi-Cheng Wang - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)
Liang Zhang - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)

Abstract: 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 $R_0 > 1$, while the disease goes to extinction if $R_0 < 1$. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio--temporal variables.

Keywords:  Two--group epidemic model, time periodic, distributed delay, threshold dynamics, Lyapunov functional.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 35B10, 35B35, 34B40, 92D30.

Received: May 2016;      Accepted: December 2016;      Available Online: May 2017.

 References