I just finished reading this excellent blog post.

Modelling within a network isn't what I do day to day, so the refresher was very appreciated. As I watched the infected nodes spread (or not, depending on the % chance of transmission and whether a node could get re-infected or not) my mind wandered towards people who are against vaccinations.

At very low transmission rates, like 10 percent, the infection tends to die out. Whereas at higher values, like 50 percent, the infection remains alive and takes over most of the network. If the network were infinite, we could imagine it continuing on and spreading outward forever.

This should be blatantly obvious, but there are only 3 ways to stop a SIR (susceptible, infected, resistant) type of outbreak:

  1. You let the outbreak runs it's course through your population. (lots of kids will die)
  2. You convert a high number of susceptible nodes into resistant nodes. (vaccinate)
  3. You prevent the infection from occuring at all. (probably the best way to achieve this is of course to vaccinate over a few generations)

I highly recommend you read it and play with the interactive examples.