American Institute of Mathematical Sciences

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

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  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.
Keywords: Tick-borne disease model, global stability..
Mathematics Subject Classification: 34C60, 34D23, 92D3.
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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