Oscillation and global asymptotic stability in a discrete epidemic model

In this paper, we study the oscillation, global asymptotic stability, and other properties of the positive solutions of the difference equation x(n+1) =(1 - Sigma(j=0)(k-1)x(n-j)) (1 - e(-Axn)), where A is an element of (0, infinity), k is an element of {2, 3....}, and the initial values x(-k+1), x(-k+2),..., x(0) are arbitrary real positive numbers such that Sigma(j=0)(k-1) x(-j) < 1. (C) 2003 Elsevier Science (USA). All rights reserved.