Which is to say that you’re both correct and incorrect. True, we don’t see smallpox in the wild anymore. That’s not because we’re all immune - in fact, we’re not. I’m 37, and neither myself nor most of my agemates or anyone younger than I is immune if we live in the US. Vaccinations for smallpox stopped in the 70’s. We have no more immunity to smallpox than the Native Americans did when Europeans first brought it here.
The reason we don’t have smallpox is because the generation BEFORE us was successfully vaccinated en masse. And **Zsofia **is right - animals don’t get, carry or transmit smallpox, so there were no smallpox viruses hiding out in birds or pigs or monkeys or anything else. That left the only living smallpox viruses in laboratories. As long as they stay there, no one will get smallpox (unless there’s another random mutation of the cowpox virus, but that’s not a huge risk.) So no one can catch it now…but if some of the virus is stolen and turned into a weapon, we’re screwed. At least until we can whip up some new vaccine doses.
Other reasons smallpox was comparatively easy to eradicate:
Smallpox has a low transmission rate. It’s actually pretty hard to catch smallpox from someone. Rather, it used to be hard to catch. There’s some evidence that it would be easier to catch it today with modern buildings and HVAC systems. But that wasn’t so much the case when smallpox was at its worst.
Smallpox isn’t communicable while it’s incubating. You’re not contagious until you have symptoms, by which time people can avoid you like…well…you know…
Smallpox was easy to diagnose. Nothing else looks quite like it. So those who had it were quickly quarantined away from other people, and those who didn’t have it but lived near a victim could be vaccinated.
Smallpox also had only one strain. There were not different smallpox viruses with different mutations, like there are for the flu virus. This means that the one single vaccine worked to prevent ALL smallpox, not just some of them.
Smallpox had no latent phase. That is, you got it, you got sick, you either died or got better. If you died (about 30% mortality rate), you’d no longer spread it. If you got better, you no longer spread it. Compare this to, say, hepatitis, where you can walk around for years not knowing you have it but spreading it to others.
Smallpox was that perfect storm of a virus that was ideal for vaccine based elimination. That it happened to be the first vaccine was actually a bit unfortunate in some ways, as it set pretty unreasonable expectations for vaccination thereafter.