Can my son catch the same bug within a week?

Last week my son got the "stomach flu" which has been going around in my area. Well, he's been completely over it for about 6 days. Last night I heard news that a friend of mines son has it. The two have not been in contact, but I have been around the other child. How likely is my son to get the same bug within a week? Is his immunity from having it, enough to make sure he doesn't get it again?