Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 87519, 10 pages
doi:10.1155/2007/87519
Research Article
On a Discrete Epidemic Model
Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, Serbia
Received 3 August 2006; Revised 5 November 2006; Accepted 6 November 2006
Copyright © 2007 Stevo Stević. 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 investigate the global asymptotic behavior of solutions of the difference equation xn+1=(1−∑j=0k−1xn−j)(1−e−Axn), n∈ℕ0, where A∈(0,∞), k∈{2,3,…}, and the initial values x−k+1,x−k+2,…,x0 are arbitrary negative numbers. Asymptotics of some positive solutions of the equation are also found.