A day before I am supposed to give an invited talk at a conference, I find myself battling an awful flu. Can someone help me figure out the right etiquette here? Do I tough it out and travel to the conference to give the talk anyway (and risk infecting dozens of people), or pull out of it citing bad health?
If you're seriously ill and risk either your health or the health of the audience, the correct course of action is to cancel. Just remember to add many apologies to the email/phone call.
It's up to the organizers of the conference to manage risks -- including cancellations, and if they did a poor job at risk management, they'll know better next time.
Edit: By 'many apologies' I mean 2-3. One at the beginning of the message/call, one at the end.
How about trying to arrange to give the talk via Skype? It won't be as good, but for sure sounds preferable to disappointing the organizers and others who may have been hoping to hear what you have to say. You can also make it a bit shorter, citing your health. The point is to make the best of the situation and show you are making a sincere effort to deliver on your promise. If you do that, it's hard for me to believe that anyone would think less of you for not physically showing up in a situation like this.
Edit: to address PeteL.Clark's comment, I agree if the flu is bad enough then clearly it will be better to simply cancel the talk, and OP should not hesitate to do this if necessary for health reasons. I did not mean to suggest otherwise. My suggestion pertains to a scenario where OP feels well enough to deliver at least a short (say, half an hour instead of an hour) talk via Skype. After all, what one would describe as an "awful flu" in the context of a dilemma about whether to travel to a different city with an overnight stay, might not seem so awful that one cannot make it to a room in one's house with a computer and deliver a short Skype address.
It's also worth pointing out that staying in a good mood is also important for one's health and recovery. If missing the talk would cause OP an excessive amount of worrying or anguish, and if by contrast giving the talk would result in a good feeling that he has been able to do something worthwhile despite having the flu, that's another argument in favor of making the small physical effort (with a potentially large mental reward) of giving a short Skype talk.
I assume you don't have anyone who could deputise for you?
If someone else from your group is going (or can take your place), is sufficiently familiar with the material, and has time/experience/willingness to adopt your talk, the organisers may be pleased to have them speak in your place.
This is not uncommon in ordinary talks. It's rare in invited talks but I have seen it done.
Perhaps ring them up and talk to them in person and see what they say to get an impression what the pressures are. It's not pleasant to forgo an invited talk, and reasonable organisers can assume that the invitee will not drop out lightly.
If you still decide to travel, nevertheless, try to stay out of clumps of people to - as you say - avoid infecting them.
That being said, being ill at a conference is very unpleasant (I am not talking even about risks here). I have fallen seriously ill on conference only once (as far as I can remember), but that was an experience I'd rather do without. You are away from people that can help you, all on your own, in a strange city, not knowing possible doctors/pharmacies, and you cannot even make use of the time to socialise with your peers (of course, an invited talk is in the stronger category of duty).
Some of the answer also depends on how long and tortuous the trip is. You say, it's one day before your talk. A single-day trip could be seen differently than a multi-day one, but the principles above still apply.
If your illness is serious then, by all means, you need to cancel invited talk, but with proper explanation, of course.
You probably want to email/phone your contact, apologize, explain situation and (if you prepared slides or material) send it to them, as a proof of your preparation and good will.
Each serious conference board should be able to handle risks, such as invited guests not appearing for various reasons.
p.s. Be aware that, depending on your health state and type of conference you might get proposal to appear "virtually", over Skype or any other means of communication.