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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Extinction and uniform strong persistence of a size-structured population model

Pages: 831 - 840, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017041

 
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Keng Deng - Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010, United States (email)
Yixiang Wu - Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States (email)

Abstract: In this paper, we study the long-time behavior of a size-structured population model. We define a basic reproduction number $\mathcal{R}$ and show that the population dies out in the long run if $\mathcal{R}<1$. If $\mathcal{R}>1$, the model has a unique positive equilibrium, and the total population is uniformly strongly persistent. Most importantly, we show that there exists a subsequence of the total population converging to the positive equilibrium.

Keywords:  Size-structured population model, basic reproduction number, extinction, uniform persistence.
Mathematics Subject Classification:  92D25, 35B40, 35L04.

Received: August 2015;      Revised: January 2016;      Available Online: December 2016.

 References