I think it would be more fun if there was a mechanic that balanced out the inevitable end, some way of slowing the spread down later in the round and give the player a way to "Win". If you took this same concept and then made it that you have to hold off the spread for a set time limit and once you reach the time limit you past that round then can move on to a more difficult level where the virus starts stronger at the beginning I think it would create a good game loop that people can get hooked in to.
Nice idea, and good work getting it put together and submit to a solid working state.