I agree about making sure your characters are okay with zombie apocalypse game. It's not everyone's cup of tea ... and even if they are into it... fighting four year old zombies? Earth's population ends because all kids are zombies by age 4? Or one? I mean, sure, most of them can't walk very well, and humanity could be saved by very large staircases (elevator buttons would be out of reach) and the return of playpens, but are your average zombie apocalypse fans going to enjoy taking the machine guns to face a crawling mass off toddlers invading the streets and day-cares of the world? Sure, they'll bite some adults, parents and caregivers, before it's figured out, but doesn't really leave you with only the deadbeat dads on the side of humanity? ...which is sort of an oxymoron ....
Well, anyway, I think the doctors and nurse idea or the special task force investigating terrorists would do for the Umbrella situation. For space meteorites spreading disease, I'd say the doctors and nurses would still work, or possibly an X-files team that thinks they are fighting possible alien invaders. Which they might very well be, if the zombie plan is the first attack. (I mean, how long do zombies last?)
For the baby zombie swarm attack... I got nothing. I can't even wrap head around it. Unless your characters are supposed to cure the baby zombies... but even then... I can't see the adventure as something folks are anxious to play. I'm not a zombie fan myself, but always pictured the typical zombie RPG player as someone who liked to blow things up, and then shoot them and then blow more stuff up. With some arson thrown in. I'm not sure baby zombies would be what they were hoping for.