Author: Sara Habibipour

Well, this blew up quickly...

Schools/workplaces are closed (California schools may even be out the rest of the year), Trump declared a national emergency, the stock markets have been up and down, and medical scientists are racing to develop a vaccine for the Coronavirus, a crown-shaped RNA virus (hence the name) that has so far infected 198,513 globally (as of March 17, 2020 9:30 pm PST) with the largest infection rates in China, Italy, and Iran.

So, what does this mean? How long will conditions be like this?

Well, no one knows for sure, of course. But, epidemiologists can try and trace Coronavirus trends using math! Yayyyyyyyyy math!

The coronavirus is growing exponentially. I bet you've heard that term before in algebra class. But, just in case we forgot, exponential growth means that as we go from one day to the next, the number of Coronavirus cases is multiplied by the same constant (a number). This is just how viruses reproduce (as long as they are in stable environmental conditions); it's nothing new. What causes new cases are existing cases. As of right now, this constant seems to be between 1.15 to 1.25 of the number of cases the previous day (of course, this isn't a definitive number, as not all cases are reported). Therefore, we can conclude that the equation for the growth of Coronavirus cases is:

ΔN = E x p x N

where ΔN=number of cases on a given day

E=average number of people someone infected is exposed to each day

p= probability of each exposure becoming an infection

This is quite concerning if you continue to draw out the line of best fit, as data has shown that cases multiply by 10 every 16 days on average (once again, this number could very well change). That would mean hitting 1 billion cases in 81 days. Yikes.

But, we can't just draw out a line forever. It has to slow down. But when? Coronavirus has already surpassed SARS which capped out at 8,096 cases. But will it be as destructive as the Spanish Flu which affected 513 million?

First of all, we have to take into consideration that when an infected person comes into contact with multiple people, not all of them are going to be new cases, as some people will already be infected. So, a better equation would be:

dN/dt = c(1-N/pop.)N

This is because there is no truly exponential curve in everyday life. They just keep going. So, the number of Coronavirus cases would be most comparable to a logistical curve where it eventually levels off. The inflection point on the logistical curve is the point where the slope stops increasing and stays roughly constant before it starts decreasing. The growth factor (New cases in one day divided by the new cases the previous day) during the increasing part of the graph would have to be bigger than 1 (1.15-1.3 ish). The inflection point would occur when the growth factor decreases to 1, meaning that the number of cases is staying constant.

So when will this happen? Well, no one really knows. But hopefully, the closure of businesses, schools, and the notion of social-distancing will spark the inflection period.

And fear? Well, a little may actually be healthy. That's for another post.

Hope you learned something from this post! Thanks for reading!

(And thanks to math class for addressing this problem for us to work out!)