Question: I am a junior at a large state university. Lately, as you all have probably heard, the coronavirus is spreading like a wildfire and we all should be scared.

My instructor is from China, and my school is also filled with Asian students. How do I ask for excused absences so that I can stay at home for the lectures so that I won't get the virus from my instructor or my Asian classmates? Do I contact the chair of the department that's offering the course or the dean of the school? Would it be better if I ask to switch to an online class instead (it's already after the add/drop period)

Some suggestion would be helpful.

Answer: 
You should do none of these things and we should not all be scared. This would be panic reaction.

You have not said in which country you are studying, but the Health authorities of most governments have issued official advice to their citizens which you should follow. Most institutions, such as universities, will also have issued official advice which you should also read and follow.

If you are in the UK the Department of Health has provided advice to UK universities.

If you wanted personal action, using hand cleansing gel dispensers provided by the university will reduce incidents of cross contamination and ensure regular hand-washing is your best defence.
If you have a special need, such as an immune deficiency, and must avoid all potential sources of infection, then your university will probably have some procedures to accommodate you. If you have deep psychological fears of disease then your university may have a counseling office to help you deal with your fears. 

Otherwise, the other answers here, counseling you to relax should be considered as good advice. 

Note, of course, that authorities are dealing with the problems of international travel by isolating travelers who might have become infected so that the problem is contained. It isn't Asians you need to be concerned with in any case. It is those frequent international travelers who don't comply with quarantine guidelines.