Okay, let me tackle this:
1) I don't think it is necessary "rude", but I do think that it is not your job to tell others to leave if they aren't feeling well, unless they are in your house. Depending on where you work, it may be necessary that they come in on that day, especially if it relates to a deadline, retail (especially food-related), or that they are so busy that is the only time available they have to come in. You don't necessarily know their circumstances, so you telling them to leave, in my opinion, is like saying your emetophobia is more important than any circumstance in this other person's life that meant she had to go into your place of employment. Although this person staying may cause you to be anxious, it is your problem, and not that person's problem.
2) I do think that you telling them to leave would be a setback, as it is avoidant behaviour. You are allowing yourself to avoid a situation which would make you uncomfortable, which will likely make you even MORE anxious the next time you are faced with it. We come in contact with sick people, like it or not, on a regular basis. If you start avoiding everyone who mentions that they feel a bit off, you are just setting yourself further back. That, and it's pretty much something that you can't control. I bet you that you have come in contact with someone who felt ill today and didn't even know it- not everyone advertises. All you can really do is worry about yourself, and take the proper precautions to prevent yourself being ill. You can only take care of yourself, as it's impossible to avoid coming in contact with people who are ill.
Have you checked out the Q&A forum? There is a sticky post where a microbiologist answered a lot of questions related to stomach viruses. It should help to alleviate a lot of anxiety, as these things aren't something you can catch just by standing next to someone, or breathing the same air.
As for why people go out in public when they feel nauseous- you have to look at it from their perspective, not your phobic perspective. For someone who doesn't fear this, nausea is just an inconvenience, and doesn't always justify putting your life on hold. I only fear others vomitting- so when I am nauseous myself, I sometimes still have to go out and get things done, whether it be laundry, going to class/work, getting groceries, etc. To me, unless it's to the point where I can't leave the bathroom for more than 5 minutes, it's not a big enough deal to justify me not doing what I need to do.
That, and I know with a lot of single parents, even if they are sick the kids still need to be picked up from school, groceries need to be bought, etc. With my friends, these things outrank their own discomfort.
As for why people don't always make it to the bathroom- I know that for myself with diarrhea I get more of a warning, and it's easier to hold off until a bathroom is available. I generally always make it to the bathroom when sick, but everyone's system is different, and not everyone gets a lot of advance "warning" before it occurs. That, and people who vomit very infrequently may not read the warning signs correctly, and it ends up as more of a surprise. I doubt that anyone wants to vomit in public, or not make it to the bathroom- but sometimes it really can't be helped. In situations such as this, please try not to blame the person, as they likely didn't want this outcome either.
I seriously think that people reacting badly to someone who vomits in public, especially if they are a kid, can be one of the events that can put people on the path of becoming emetophobic themselves. The shame, embarrassment, and idea that they did something "bad" can stick, and make them focus on the event, and fear it occuring again.
Hey- I see that you're new- welcome to the site!
oh, and you avatar is hella-cool
*amber*
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