Global stability of equilibria in a tick-borne disease model

2007, Volume 4, Issue 4: 567-572. doi: 10.3934/mbe.2007.4.567

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1.
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899

Received: 01 April 2007 Accepted: 29 June 2018 Published: 01 August 2007
MSC : 34C60, 34D23, 92D30.

In this short note we establish global stability results for a four-dimensional nonlinear system that was developed in modeling a tick-borne disease by H.D. Gaff and L.J. Gross (Bull. Math. Biol., 69 (2007), 265--288) where local stability results were obtained. These results provide the parameter ranges for controlling long-term population and disease dynamics.
- Tick-borne disease model,
- global stability.
Citation: Shangbing Ai. Global stability of equilibria in a tick-borne disease model[J]. Mathematical Biosciences and Engineering, 2007, 4(4): 567-572. doi: 10.3934/mbe.2007.4.567

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Abstract

In this short note we establish global stability results for a four-dimensional nonlinear system that was developed in modeling a tick-borne disease by H.D. Gaff and L.J. Gross (Bull. Math. Biol., 69 (2007), 265--288) where local stability results were obtained. These results provide the parameter ranges for controlling long-term population and disease dynamics.
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