On a Discrete Epidemic Model

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