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

Yoshiaki Muroya

doi:10.3934/dcdss.2015.8.999

Article Contents

2015, Volume 8, Issue 5: 999-1008. Doi: 10.3934/dcdss.2015.8.999

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

Yoshiaki Muroya^1,

1.
Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555

Received: November 30, 2013

Revised: February 28, 2015

Published: October 2015

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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.

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Mathematics Subject Classification: Primary: 34K20, 34K25; Secondary: 92D30.

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