# American Institute of Mathematical Sciences

2007, 4(4): 567-572. doi: 10.3934/mbe.2007.4.567

## Global stability of equilibria in a tick-borne disease model

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

Received  April 2007 Revised  July 2007 Published  August 2007

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.
Citation: Shangbing Ai. Global stability of equilibria in a tick-borne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567-572. doi: 10.3934/mbe.2007.4.567
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