Host Extinction Dynamics in a Simple Parasite-Host Interaction Model

Tzy-Wei Hwang; Yang Kuang

doi:10.3934/mbe.2005.2.743

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2005, Volume 2, Issue 4: 743-751. Doi: 10.3934/mbe.2005.2.743

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Host Extinction Dynamics in a Simple Parasite-Host Interaction Model

Tzy-Wei Hwang^1, and
Yang Kuang^2,

1.
Department of Mathematics, Kaohsiung Normal University, 802, Kaohsiung, Taiwan, R.O.C.
2.
Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804

Received: June 2005

Revised: August 2005

Published: September 2005

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Abstract

This short article carefully formulate a simple SI model for a parasite-host interaction through the basic birth and death processes analysis. This model reveals and corrects an error in similar models studied recently by various authors. Complete mathematical investigation of this simple model shows that the host extinction dynamics can happen and the outcomes may depend on the initial conditions. We also present biological implications of our findings.

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Mathematics Subject Classification: 34C25, 34C35, 92D25.

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