In this post, I will use one graph to explain why COVID-19 is so hard to understand, and therefore to fight. It shows the daily confirmed COVID-19 cases in the US, and the 5-day change in daily cases, since the end of April:

The blue curve at the bottom shows daily confirmed COVID-19 cases in the US. It shows an initial drop to about 20,000 cases, then the "summer rise" to about 70,000 cases per day in July, another drop to about 40,000 in September, and then a rise to 170,000 cases per day in November.

The red curve, which uses the y-axis on the right, shows an indication of the growth (or drop) in cases: the ratio of cases on a given day, divided by the number of cases 5 days earlier. When this ratio is below 1 (in the green section), case numbers are going down; when it is above 1 (in the light red section), the number of cases is increasing.

The numbers are based on 5-day periods because that is the roughly the average time between getting infected, and passing the infection on to someone else. In scientific jargon, this is often called the "generation interval" or the "serial interval". One way to understand it is to remember that it typically takes about 5 days after infection for symptoms to start, and that the chance of infecting others is largest just before and just after first symptoms.

This means that the 5-day ratio is also very close to the "reproductive number", often called R. In practical terms, R indicates how many others, on average, each infected person infects. If each person infects more than one other person, the number of new infections per day grows; if each person infects less than one other person, the number of daily infections goes down. This can be easily seen in the graph, where the red curve is in the red area whenever the number of daily cases (the blue curve) goes up.

Now take a close look at the values we get for R. In May and August when case numbers were dropping, R was between 0.85 and 1. In the summer and fall periods where case numbers were increasing, R was above 1, but never higher than 1.3. Typical values around 0.9 in "dropping" periods, and around 1.2 in "rising" periods. The difference is *quite small *- and **therein lies the problem**! To understand why, we need to look at this from two angles: the "personal risk" perspective, and the "public health" perspective.

### Personal risk: A small increase means very little

When deciding what to do, in a public health crisis, the first question most people will ask is "What is the risk to *me*?" Depending on the answer, and on personal tolerance for risks, they may be inclined to change their behavior more or less. But regardless what *exactly* the answer is, everyone will have to accept a *certain* level of personal risk in the end.

After a few weeks or months of "being good" and, for example, staying away from restaurants and bars, the desire to go back to normal becomes stronger and stronger, and we start doing things again that are slightly more risky. That might be going to restaurants again; meeting with friends; going shopping; not wearing that face mask; or something else. But we'll generally decide that a bit more risk has to be taken. If we are young or healthy, we may well conclude a slight *increase* in risk still means a *very low* risk of getting seriously sick. Unless you're a statistician, you probably won't quantify the risk, but just about anybody would agree that a relative risk increase from 0.9 to 1.2 is so small that it's worth taking, if it means we can go back to the gym, the hair dresser, shopping, restaurants, or whatever strikes our fancy. If my personal risk was small to begin with, then even a 2-fold or higher increase in risk may well be worth it.

On a personal level, taking a bit more risk is a *perfectly reasonable* decision. This also is true if we consider others in our risk assessment, too - kids we send to school, other family members, or friends we meet.

### Public health: Small risk increases have disastrous consequences

But what happens if everyone decides that taking a bit more risk is perfectly reasonable, and changes their behavior a bit? Say, for example, in a way that increases the risk of getting COVID-19 by just one third. What happens?

Let's assume we were in a period were new infections were dropping by 10% every 5 days, corresponding to R = 0.9. With 1/3 more infections now, R increases to 1.2: instead of a steady drop, we now have a rapid rise in new infections: 20% more daily infections after 5 days, and 44% more daily infections after 10 days (1.2 x 1.2). After a month of R staying at 1.2, the number of daily infections has grown 3-fold: just about what we saw in the US from October to November. **A very small change on the individual level has caused a huge increase on the population level. **

What is a perfectly reasonable decision on a personal level becomes a public health disaster.

### Small things are "driving the pandemic"

Currently, the US is just one of many countries that is failing to control the resurgence of COVID-19 infections. A common theme here is that many regions try to contain COVID-19 with a minimal set of measures, for example limited restaurant hours instead of full closures. Against many measures, an often-heard argument is that "X is not driving the pandemic". Various regions have used this argument to leave schools and colleges open, have restaurants operating with minimal or no restrictions, and so on.

Taken literally, the arguments are correct insofar as that each individual "infection place" like schools or restaurants is *not* causing the *majority* of new infections. But even measures that eliminate just a small percentage of new infections can make a huge difference, and a few in combination can make the difference between a controlled epidemic with dropping infection numbers, and a rapidly growing, out-of-control epidemic. Therefore relaxing a few of such "minor impact" measures may well end up "driving" the epidemic from a "dropping" phase into a "rapid growth" phase. This problem is only made worse by halfhearted interventions, which drop R only just below 1.0. This means that case numbers will drop only very slowly, and rapid growth resumes quickly again after any relaxation.

Over the past six months, I have read several hundred scientific publications about COVID-19. Of all these, one of the publications that stuck to my mind the most was published by scientists from New Zealand. Apparently, it formed the basis of New Zealand's successful *complete elimination* of COVID-19 cases in the country. It listed a large number of interventions which were used in groups, depending on the current level of infections:

*avoidable*COVID-19 deaths.