Thank you Enrique! You make very interesting points, I started to read your post but it will take me a while to process it because it has so many updates and material spread in the comments, and the long discussion section in there seems very relevant too. The first thing I noticed is that in your model you make different simplifications to the “full” delayed set than I did, but they both give reasonably good fits. I hope you can add soon the code to learn how you dealt with the fit problem. I had my own code spread over a dozen files, so if you work like me, I understand its complicated to gather the essential parts in one single presentation.
I agree with you that what we have developed is a “model of the data” and conclusions about the epidemic characteristics are not straight forward and must be done with care. For example, the derived periods include the time it takes to report, which in some countries can be considerable. Some case detections are done with (cheaper) tests that measure antibodies after you are almost recovered. Others with the PCR method which detects genetic parts of the virus and therefore works even in very early stages of the disease, when still latent. The latter will have little chance to infect others from a strict quarantine, but the first probably already did. On top of that, there is strong evidence that the large majority of cases are asymptomatic, and to our knowledge they are also capable to infect others, to some extent. One might think of the detected, symptomatic cases as the tip of the iceberg that gives you a measure, a “tracer” of the total infectious population. In that sense, I believe the I-curve does represent the infectious group to a good approximation.
I look forward to read your take on why the population size has to be small. I wish this could be derived from the level of stringency and ultimately to have a model that helps you find a cost-effective optimum level for these measures.
