Hopefully, most people who have a severe cold stay home to recover rather than going in to the office and risk spreading the cold to coworkers.
Unfortunately, there are times when deadlines must be met or there are no more sick days to use. In these cases, an ailing individual would most likely prefer to be home as much as you don’t want them at work.
How should you deal with working next to an ill coworker? Do not complain. Mind your own business, take extra vitamin C, eat well, and get plenty of rest. If space permits, find an area to work in away from your coworker. You may even want to consider scheduling appointments out of the office during this time.
Doctors also highly recommend washing your hands frequently with soap and water for a minimum of 30 seconds.