I think I've actually played that before, you have an incubation period once someone is infected and if they're not killed or lynched before then, they can start infecting people as well. You can do all kinds of shit, have everyone choose to infect someone but only those with the virus achieve it, announce how many people have it etc.
I guess the negative of it is that it's harder to pinpoint a game strategy for working out who has the virus if people don't know it. You'd probably be best setting it up with one or two (depending on numbers) being infected and then spreading it from there. And you can do fun shit with immunity, the doctor role etc.