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 xn+1 = 1 − k−1 j=0 xn−j (1 −e−Axn ), where A ∈ (0,∞), k ∈ {2, 3, . . .}, and the initial values x−k+1,x−k+2, . . . , x0 are arbitrary real positive numbers such that k−1 j=0 x−j < 1.  2003 Elsevier Science (USA). All rights reserved.