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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 573146, 6 pages
http://dx.doi.org/10.1155/2015/573146
Research Article

Global Stability of an Anthrax Model with Environmental Decontamination and Time Delay

Department of Mathematics, University of Zimbabwe, P.O. Box MP 167, Harare, Zimbabwe

Received 17 March 2015; Accepted 21 June 2015

Academic Editor: Mauro Sodini

Copyright © 2015 Steady Mushayabasa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Anthrax occurs worldwide and is associated with sudden death of cattle and sheep. This paper considers an epidemic model of anthrax in animal population, only. The susceptible animal is assumed to be infected, only, through ingestion of the disease causing pathogens. The proposed model incorporates time delay and environmental decontamination by humans. The time delay represents the period an infected animal needs to succumb to anthrax-related death. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model fully hinges on whether the associated reproductive number is greater or less than unity. The effectiveness of environmental decontamination on eradication of anthrax in the community is explored through the reproductive number.