We all know how annoying and vexing the common cold virus can be, particularly during the winter season. Nobody likes that runny nose or that constant urge to sneeze; nor is the coughing, headache, or scratchy throat anything to write home about. To avoid catching the common cold, we know that we should wash our hands often and keep from being breathed or sneezed on by those already infected. Yet despite all our efforts, we still seem to get that yearly cold. Maybe mathematics has some clues as to how we might lessen our chance to pick up that awful cold.

The cold virus is transmitted through droplets that are expelled by infected people’s coughing and sneezing. Once the virus-laden droplets are emitted into the air, they form a cloud of infection that can last for hours. In addition, the expelled droplets fall on surfaces from which others pick them up and then infect themselves, as through touching the nose or eyes. Interestingly, the virus is easier to recover from non-porous surfaces like metal and glass, rather than porous surfaces like wood or paper. From a microscopic perspective, viruses have less “pockets” to hide in on non-porous surfaces than on porous ones. Since many people are infected through hand contact, it sure would be nice if we could keep our hands free from that nasty cold virus so that we wouldn’t be the next one starting the chain of infection. But what does this have to do with math?

Since we spend a lot of time indoors during the cold months and do things like shop in busy malls and other public places, and since the cold virus is more active during the winter, we are more likely to touch a contaminated door handle than during the spring and summer seasons. When we enter busy stores, we have to push or pull on doors which either have non-porous handles or metallic center plates. These make for good areas where the nasty cold virus might be lurking. In fact, from a probabilistic model, you can be quite certain that the cold virus will be found somewhere on those door handles. Thus given this knowledge, how do we use a little math to decrease our chances of inoculating ourselves with the common cold?

Well let’s take a look. If you are opening a door with a handle, you would do well to stay away from the center areas as more people will touch the regions that provide easy access to the door and provide easy opening. If you have to push open a glass door, or one with a center metal plate, keep from touching the central portion of the plate, or push the door either above or below the center area or closer to the hinge. Pushing the door closer to the hinge will require more effort, since from a physics perspective you are creating less torque and therefore need to push harder. However, you might have more energy two days later when you don’t come down with that ugly cold that you would have, had you pushed further away from the hinge.

Yes. Simple math says that the probability of cold germs inside those central areas is much greater than outside of them. Consequently, you are much safer outside the high density areas where everyone places the hands. In this situation, by using the probability of area, we can minimize our risk of infection. Even if one person with infected hands touches that central area of the door plate or handle, the virus will stay active for hours. The next few people who come along and touch that region and then touch their eyes or nose...bam! Another cold.

Thus once again math comes to our aid to help us in our everyday life—in this case by keeping us healthy. And who knows? This knowledge just might keep you from getting something more serious like the flu, which at the extreme end of the spectrum could possibly kill you. Heaven forbid! So do yourself a favor and become a friend of math. It could just save your life.

Joe Pagano