1. Diffusion in a Watts Strogatz model (25pts)

Download the netlogo model SmallWorldDiffusion.nlogo and experiment with modifying the parameters. It is an SI model (nodes are susceptible or infected, and once they are infected they remain infected).

What effect does increasing the rewiring probability have on the speed of diffusion. Qualitatively explain why this is so.

2. Diffusion in a Barabasi-Albert graph (25pts)

Download the netlogo model BADiffusion.nlogo. Compare the rate of diffusion at gamma=1 (random attachment) and gamma = 0 (preferential attachment). Qualitatively explain why the behavior is different.

Extra credit (10pts)

Modify either of the models to make them into an SIS model with each infected node having a probability r of recovering (and moving back into the susceptible population) at each time step (and so not infecting its neighbors at that time step). Set r to be 0.2. Can you find a critical transmission probability p below which the model does not exhibit epidemic outbreaks? Give the value of your other parameters as well (e.g. number of nodes, gamma ,rewiring probability).