Host Extinction Dynamics in a Simple Parasite-Host Interaction Model

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

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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: 01 June 2005 Accepted: 29 June 2018 Published: 01 October 2005
MSC : 34C25, 34C35, 92D25.

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.
- host extinction,
- global stability.,
- Parasite-host interaction
Citation: Tzy-Wei Hwang, Yang Kuang. Host Extinction Dynamics in a Simple Parasite-Host Interaction Model[J]. Mathematical Biosciences and Engineering, 2005, 2(4): 743-751. doi: 10.3934/mbe.2005.2.743

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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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