By Tim Chartier @timchartier

What does the viral activity in social media have to do with the coronavirus? Both are viral, although in very different ways. While vaccines offer hope, we are still in a time where social distancing plays an important role. Hospitals are overwhelmed, and the importance of flattening the curve is ever-present. Let’s see how looking at staggering rates of social media activity can increase our understanding of growth rates, the need for social distancing, and flattening the curve.

Let’s begin with a social media phenomenon that became known as the Instagram Egg. It all began with a post on the @world_record_egg Instagram account. The photo of a simple brown egg sitting upright against a white background was originally taken by Serghei Platanov. Simple enough. Let’s focus on the viral growth of the number of likes for the post of the simple egg. On January 4, 2019, the @world_record_egg account was created with the post:

A simple egg with the caption, "Let's set a world record together and get the most liked post on Instagram. Beating the current world record held by Kylie Jenner (18 million)! We got this." At that moment, the post began with 0 likes. It took ten days for the image to reach 18.4 million likes and become the most-liked Instagram post of all time. After an additional 48 hours, the post surpassed 45 million likes and became the most liked online post (on any media platform) in history.

How does viral growth occur? Let’s focus on the Instagram Egg. We see something and tell others or, by liking or sharing it, place it in the social media feed of others. This virtual interaction leads to exponential growth. Suppose each like on a given day leads to two new likes on the next day. We’ll begin with one like on day one. Then the like button would be clicked twice on day two, giving the post a total of 1 + 2 = 3 likes after two days. On day three, there would be 2*2 = 4 new likes and a total of 3 + 4 = 7 total as seen in the figure. On day four, we again double giving 4*2 = 8 new likes and a total of 7 + 8 = 15 likes. Continue this pattern of doubling and determine how many times the like button would be clicked on day ten. How many total likes would the post have? Spoiler alert: It won’t seem very newsworthy. 

What if this pattern continues and each new like leads to two new likes the following day? Jump ahead to day fifteen and the post would have over 32,000. Day twenty would have over a million likes. Note how quickly things move from unnoticeable to viral.   

However, compared to the rate of growth in the number of likes for the Instagram Egg, our model isn’t growing fast enough. The egg received 18 million likes in ten days and our model only reached around 1000. We would need each like to lead to six new likes on the next day to reflect the ten-day growth rate of the Instagram Egg. Let’s look at this another way. If the Instagram Egg had led to two new likes on the next day rather than six, the post would have been far from sensational and about as plain as the image in the post. So, reducing the social media interactions from six to two substantially impacts the rate of exponential growth. 

Let’s shift to COVID-19.  It is estimated that each person with coronavirus will lead to two new infections. This is exactly our first model for the Instagram Egg. Each new person infected today leads to two new infections tomorrow. From our earlier work, things would have easily been manageable on day ten. However, exponential growth via the doubling at each step led to over a million infected people on day twenty, which is too fast for health care systems to manage. 

Social distancing leads to fewer interactions and decreases the average number of infections per person. In this case, we must work to slow the rate, which is often discussed as flattening the curve. For the Instagram Egg, the rate of growth was significantly different when social media interactions reduced from six to two. 

For coronavirus, social distancing leads to fewer interactions and decreases the average number of infections per person. We just saw that an average of two people being infected per person leads to an overwhelming rate of infections. Suppose on average 1.5 people are infected for each infected person. How much of a difference would this make in twenty days? In twenty days, we would have under 7,000 total cases instead of over a million. This dramatic decrease has monumental impacts on the effectiveness of our health care system.

Of course, that would be the case if we began social distancing on the first day of infection. But we aren’t. As we saw, the total number of infections isn’t very stark even for the first ten days when the number of new infections doubles from day to day. Suppose the number of cases doubles each day for the first ten days. After ten days, we see the spread and begin social distancing. So, from the eleventh through the twentieth day, each day has one-and-a-half times the number of cases as the previous day. Then, after twenty days, we have just over 88,000 cases rather than over a million. Social distancing makes an impact on day one or day ten. 

The numbers underscore the importance of reducing interactions to slow the viral rate of growth. By social distancing or staying home, we can reduce the rate of growth to less than 1.5 infections per infected person and keep us within the capacity of our health care systems. Simply put, slowing the rate of exponential growth can help our health care systems save more lives.