I would begin by encouraging you to read the church’s official statement on communion, the statement does not directly address these issues, but it’s important background information to know as we begin discussion. The General Board of Discipleship has a webpage addressing the issue of swine flu which also applies to influenza in general.
The American Journal of Infection Control has a letter from the CDC stating that “Within the CDC, the consensus of the National Center for Infectious Diseases and the National Center for Human Immunodeficiency Virus, Sexually Transmitted Diseases, and Tuberculosis is that a theoretic risk of transmitting infectious diseases by using a common communion cup exists, but that the risk is so small that it is undetectable.” Many churches that use a common cup use real wine, but the alcohol content of wine is far below the level necessary for it to serve as a disinfectant. In addition, as stated in the letter referenced above: “a recent study [1997] of 681 persons found that people who receive Communion as often as daily are not at higher risk of infection compared with persons who do not receive communion or persons who do not attend Christian church services at all.”
The most important conclusion I drew from studying the threat of H1N1 and influenza when receiving Holy Communion several years ago is that the main problem is not the communion elements in and of themselves, but rather direct human to human contact. This presents a problem because Christian fellowship almost demands that direct human to human contact be preserved in some manner. I want to remind everyone that fist bumping (or even elbow bumping) is an alternative to handshaking and individually wrapped sanitizing wipes are available in the narthex.
Links:
Official United Methodist statement on Holy Communion: http://www.gbod.org/resources/this-holy-mystery-a-united-methodist-understanding-of-holy-communion1
General Board of Discipleship Webpage: http://www.gbod.org/worship/default.asp?act=reader&item_id=7908&loc_id=9,10,277
The American Journal of Infection Control Article: http://www.ajicjournal.org/article/S0196-6553(98)70029-X/abstract. The main disadvantage of this article is that you have to pay $14 for a copy. I paid the $14 and you can stop by the church office and read my copy.
Fist bumping vs handshakes: http://www.npr.org/blogs/goatsandsoda/2014/07/29/336272173/fist-bumps-pass-along-fewer-germs-than-handshakes