Chaotic and periodic spreading dynamics in discrete small-world networks

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, μ. 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.