On a reaction-diffusion model for sterile insect release method with release on the boundary

Xin Li; Xingfu Zou

doi:10.3934/dcdsb.2012.17.2509

Article Contents

2012, Volume 17, Issue 7: 2509-2522. Doi: 10.3934/dcdsb.2012.17.2509

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On a reaction-diffusion model for sterile insect release method with release on the boundary

Xin Li^1, and
Xingfu Zou^2,

1.
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001
2.
Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7

Received: January 31, 2012

Revised: March 31, 2012

Published: September 2012

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Abstract

We consider a partial differential equation model that describes the sterile insect release method (SIRM) in a bounded 1-dimensional domain (interval). Unlike everywhere-releasing in the domain as considered in previous works [17] and [14] , we propose the mechanism of releasing on the boundary only. We show existence of the fertile-free steady state and prove its stability under some conditions. By using the upper-lower solution method, we also show that under some other conditions there may exist a coexistence steady state. Biological implications of our mathematical results are that the SIRM with releasing only on the boundary can successfully eradicate the fertile insects as long as the strength of the sterile releasing is reasonably large, while the method may also fail if the releasing is not sufficient.

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Mathematics Subject Classification: Primary: 35J57, 35K57; Secondary: 92B05, 92D25.

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