Host Extinction Dynamics in a Simple Parasite-Host Interaction Model

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2005, 2(4): 743-751. doi: 10.3934/mbe.2005.2.743

Host Extinction Dynamics in a Simple Parasite-Host Interaction Model

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

Received June 2005 Revised August 2005 Published October 2005

Abstract
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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.

Keywords: host extinction, global stability., Parasite-host interaction.

Mathematics Subject Classification: 34C25, 34C35, 92D2.

Citation: Tzy-Wei Hwang, Yang Kuang. Host Extinction Dynamics in a Simple Parasite-Host Interaction Model. Mathematical Biosciences & Engineering, 2005, 2 (4) : 743-751. doi: 10.3934/mbe.2005.2.743

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