When a zombie is somewhere, he just has to get in touch with a healthy human to turn him into a zombie. This is called an infection.
You can be infected with many other diseases, some of them are fatal, and other are benign.
In infection games, you have to transmit diseases and use chain reactions to meet all your goals.
One of the most famous sagas of infection games is the saga of Infectonator game in which you need to turn as many people as you can into zombies.