We propose a new discrete model for the controlled spreading dynamics on Newman-Watts small-world networks. We study epidemic spreading behavior as a function of the small-world probability, p, and the nonlinear control gain, /spl mu/. We find period doubling bifurcations as well as chaotic spreading dynamics, depending on the choice of parameters. As it turns out, it is possible to restrict the spread to a bounded region via a suitable choice of control parameter, but it is not possible to erase the infected volume completely, however strong the control parameter chosen.