“When you have 15 people, and the 15 within a couple of days is going to be down to close to zero, that’s a pretty good job we’ve done.” said president Trump on Feb 26. Six weeks later, as I write this post on April 18 there have been 694,000 cases and over 31,000 deaths in the U.S. according to the Johns Hopkins Coronavirus Resource Center.

How did we get from 15 cases to these huge numbers in 6 weeks? It sounds reasonable that if we started with only 15 cases, we should have been able to isolate them, trace their contacts and stop the epidemic in the U.S. in it’s tracks.

There are two reasons why this did not work.

1. We only tested people who were very sick. It is now obvious that there were a lot more people in the U.S. that were carrying and spreading Coronavirus on February 26.
2. Basic epidemiology tells us that a contagious virus can spread very rapidly in a population which has no immunity.

Before the last two months, most of us did not even know what an epidemiologist was. Now epidemiologist has become a household word.  We all  have heard a lot of epidemiologists on television in the last two months. Sometimes they make themselves understandable and sometime it seems they are speaking Greek. This post is an attempt to translate some of the technical terms into language that most non-epidemiologists and non-doctors can understand and to begin to explain how we got from 15 cases to where we are now.

Suppose one person is infected with a virus that can spread to other people. We would like to know how easily the virus can spread. One measure of this is the average number of people that will be infected with the virus by one infected person. Epidemiologists call this the reproduction number using the symbol R. If R =1, that is, if an infected person on the average infects one other person, then the infection will continue to spread slowly, but there will not be an epidemic or an outbreak. If R is less than 1, that is if one person infects less than one other person on average, then the infection will die out and cease to be transmitted. If R is greater than 1, that is if one person infects more than one other person on average, then there is likely to be an outbreak or an epidemic. This is called exponential spread and it works like this.

If R=2, that is if one infected person on average infects two other people and if infection occurs every 4 days (this is pretty much what happened in New York) then after 4 days there will be 2 more infected people. After 4 more days there will be 4 new infections. After two weeks the number of new infections will be 2^3.5or 13 cases. After a month there will be 2⁷ or 128 new cases. After another month there will be 2¹⁴ or 16,384 new cases. After 3 months there will be 2²⁸ new cases or 268,435,456 (over 268 million). Remember that these numbers assume we start with only one case.

The number of new cases will never really get this big because the entire population of the United States is only 330 million. At some point a large percentage of the population will have been infected and either died or developed immunity. This is called herd immunity and  will cause R to be less than 1 and the infection will die out. That assumes that most people who are infected and get well are immune to the virus, at least for a while. We can only hope that is the case with the coronavirus. We do not yet know that for sure.

There are a lot of things besides the infectivity of the virus that affect the value of R. Anything that increases contact between people will increase R and anything that reduces contact will decrease R. R will therefore be higher in densely populated urban areas.  That is why we have seen coronavirus infection hot spots at the beginning of the epidemic in urban areas like New York , New Orleans and Detroit.

Having people stay home and/or having people stay at least 6 feet apart when they are outside decreases contact between people and therefore decreases R, the reproduction number.  Although these measures  may decrease R close to 1, they are not likely to decrease R to less than 1. The best we can do is slow down the infection rate to the point that hospitals don’t get overwhelmed. The only thing that will make R less than 1 is herd immunity. Herd immunity means that so many people are immune to infection that the virus stops spreading. One way herd immunity may happen is by allowing the virus to spread through the population.

Since about 1-5% of people die from infection this is clearly not a good strategy. Even a mortality of 1 % means that more than 1 million people in the US would die before herd immunity kicks in.

Another way for herd immunity to develop is to have an effective vaccine and give the vaccine to the majority of the U.S population. This is clearly the best way to completely stop the epidemic, but we are at least a year away from having an effective vaccine.

In the meantime, the only way we can decrease R, is to continue to decrease contact between people, which means to continue social distancing. Re-starting the economy, even carefully means that contact between people will increase. That increases the risk of another outbreak. It is a balancing act that will be difficult to manage.

In the next post, I will talk more specifically about SARS-COV2, which is the name of the virus that causes the disease COVID-19.