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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 434537, 10 pages
http://dx.doi.org/10.1155/2015/434537
Research Article

Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model

College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China

Received 11 March 2015; Accepted 20 May 2015

Academic Editor: Josef Diblík

Copyright © 2015 Zhijian Wei and Meitao Le. 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

We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results.