Global stability of equilibria in a tick-borne disease model

Shangbing Ai

doi:10.3934/mbe.2007.4.567

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

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Global stability of equilibria in a tick-borne disease model

Shangbing Ai^1,

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

Received: March 31, 2007

Revised: June 30, 2007

Published: July 2007

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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.

Keywords:

Tick-borne disease model,
global stability.

Mathematics Subject Classification: 34C60, 34D23, 92D30.

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