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

A Lotka-Volterra system with patch structure (related to a multi-group SI epidemic model)

Pages: 999 - 1008, Volume 8, Issue 5, October 2015      doi:10.3934/dcdss.2015.8.999

 
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Yoshiaki Muroya - Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555, Japan (email)

Abstract: In this paper, for a Lotka-Volterra system with infinite delays and patch structure related to a multi-group SI epidemic model, applying Lyapunov functional techniques without using the form of diagonal dominance of the instantaneous negative terms over the infinite delay terms, we establish the complete global dynamics by a threshold parameter $s(M(0))$, that is, the trivial equilibrium is globally asymptotically stable if $s(M(0)) \leq 0$ and the positive equilibrium is globally asymptotically stable if $s(M(0))>0$, respectively. This offer new type condition of global stability for Lotka-Volterra systems with patch structure.

Keywords:  Lotka-Volterra system, patch structure, global stability, Lyapunov functional, multi-group SI epidemic model.
Mathematics Subject Classification:  Primary: 34K20, 34K25; Secondary: 92D30.

Received: December 2013;      Revised: March 2015;      Available Online: July 2015.

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