* If each infected person infects less than 1 other person on average, we'll have stopped the spread.* This isn't exactly correct. It means that, eventually, t

* If each infected person infects less than 1 other person on average, we'll have stopped the spread.* This isn't exactly correct. It means that, eventually, the spread would die out even if there were an infinite number of potential hosts. But it's still spreading. If that number is exactly 1, ~everyone will still end up getting infected. If it's just a bit below 1, it will behave as a decaying exponential but will still take a long time to die out.