David, in response to your comment, I only know to remake the same two points as I did in my article.

It's reckless for us to suppose a model (the sigmoidal curve), as many people do, if we don't first consider the logic. I don't see the logic grounding the presumption that the sigmoidal curve will hold.

The logic I see is that an epidemic will spread through a population and take three possible courses:

  • Best: It is ruthlessly isolated, has no opportunity to spread, and goes extinct.
  • Worst: It gets everybody sick, and so has no opportunity to spread, and goes extinct.
  • Medium: It finds it difficult to spread and so the transmission rate becomes less than 1 and it dies out.


Note that currently we are at the very beginning of this pandemic, in the sense that less than 1% of the world's population has gotten sick. The vast, vast majority of the population is not immune to this coronavirus. This means that we are at risk of the worst case scenario.

In a few countries, like South Korea, through aggressive testing, contact tracing and isolation, they have achieved the Best scenario, and basically wiped the virus out.

In most countries what we see now is that different policies have slowed the spread of the virus. But the virus still spreads at a rate proportional to those who are currently contagious. The rate is basically new cases / total cases. And that rate directly reflects the effectiveness of the policies. If you change the policies, the rate will change. Why wouldn't it?

The simple logic behind the sigmoidal curve is that as the population gets sick, the virus runs out of new people, and so it can't grow exponentially any more, and ultimately, it can't grow out all. A more sophisticated way to get a similar curve is if the transmission rate is pushed below 1, then the new cases will drop down. But the latter model only holds conditionally. As soon as the conditions (the quarantine) are changed, it snaps back. It will snap back to exponential growth immediately if our conditions go back to normal.

My concern is that reliance on the sigmoidal model - or the course in other countries - is reckless if we don't sustain the policies, and especially, if we just suppose that the virus dies out on its own. It doesn't and it won't.

The question remains whether the virus will go away. It won't until there's a vaccine or until there is aggressive testing, tracking and isolating. This is a point that responsible parties have been speaking up about and getting heard. So that has put me at ease.

The remaining contribution that my article makes is to note that the indicator (new cases) / (total cases) is a very simple indicator that is much more informative than the typical data given by the WHO and the media. And that this indicator is scientifically relevant as a way to study, across countries, states and regions, what policies are achieving or not.

A conflicting hypothesis, which you may be implying, is that the virus basically takes the same course in each country. That could be examined, for example, to see what the logistic curve (or the bell curve) looks like in each country. But it is immediately obvious that the curve for South Korea is completely different than for the US. So if it's not the virus, then it must be the policy. Or what?

I suppose that a problem I see built into the sigmoidal curve is that it is, like any model, a presumption. It presumes the virus will die out, and then if the virus doesn't die out, then it says, well the conditions changed. Whereas the model for exponential growth presumes exponential growth, and if the rate changes, then it says, well the policy changed. Personally, the latter model seems much more relevant and responsible because it focuses on what's happening now (the rate of growth) rather than some presumptive end in the future (when will this peak, when will this be done). Given the instability of these models, it seems much more pertinent to focus on appreciating what is happening now, what that depends on, what that entails. Is the exponential rate going down? seems to me a much more useful way of thinking than How accurately can we predict the peak? But that's my personal bias, worrying about whether we are doing enough, rather than trying to argue why we can finish with this. Because I look at the underlying logic and conclude that we aren't doing enough until we are actively and completely stomping it out.

It's like looking at a burning house and asking if the flames are going down. And saying, well, the flames are dropping so we don't need any more water.

I am just restating myself. But I may ask, am I understood? Does that help or not? Is there something I'm not understanding?