Did you solve it? How many will the zombie outbreak infect?

Will we all be eating brains by sunset, or will the virus die out of its own accord? Here's the solution to today's puzzle about the zombie virus

Earlier today I set you a Halloween puzzle with the following set-up:

An infected zombie has a 1/3 chance of passing the infection to a single human, a 1/3 chance of passing the infection to two humans, and a 1/3 chance of passing the infection to no one. No one in the UK is infected by the zombie virus until a single zombie arrives.