It would be interesting to run the freeloader situation with 1% freeloaders, 2% freeloaders, ..., 99% freeloaders, each 1000 times, and plot the probability that more than half the population are eventually infected as a function of the number of freeloaders.

I'm thinking the graph will show a sharp spike at a critical transition probability because it's a similar model to percolation [1].

In fact I may write my own simulation for this.

[1] http://en.wikipedia.org/wiki/Percolation_threshold