I have an 8 year old who worries about this (and many other things - he's such a worrier) from time to time. We try to tackle it primarily from a practical angle, and also add religion.
The ladies here have offerred excellent advice! I love Cheryl O.'s advice about pointing out all the others who have predicted the end of the world, and were wrong. We have gone over that in our home. We also talk about how we live every day the best possible way, and don't live our lives worrying about things we can't change. I'm not a worrier, so sometimes it's hard for me to understand why he gets so upset, but it's heartbreaking at the same time. Prayer helps him get through it sometimes. He's a devout little Catholic. :)
We haven't tried the survival kit, but that's not a bad idea. I may try that next time he goes through a worrying spell.
Good luck with your little guy!