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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.

Excellent, you have in a sense rediscovered what I proposed in my post a couple or more months ago (https://community.wolfram.com/groups/-/m/t/1904319), that using delays works best - although it makes the fitting more time consuming - and you have taken it one step further. I haven't posted the notebook that makes the automatic fits, so it is good that you do! I just haven't had time. In my post I discuss (in a discussion with Robert Nachbar) why the population has to be small. An article is forthcoming.

You should make a mental note that models which fit the epidemiological data as you propose (if I understand you correctly, as you do not really discuss what your data are) are not truly epidemiological models. For that you need to consider an alternative way of fitting the data in which the detected infections are matched to the R curve of the models (since you effectively put those individuals into quarantine and remove them from the infection chain). It is also possible to do that and get good fits (you can see that in my post).

And you can make models that fit the fatalities data as well in a similar vein (I owe the explanation for this and for why it works).

By the way, you can eliminate the manual guessing of initial values for the minimization procedure by automatically honing in on the right values, to the precision you want. It takes a long time to find the values like this (4 hours in case of the simplified SIR with delay model I use the most).

Excellent job!

It might work, I tried different nonlinear terms but I didn't think on using log(S), thank you for the feedback, I will check it out!

Thanks Robert! I share your concern about the reduced total population, something I briefly comment in the Discussion, and I’ve been thinking about ways to do it in a less artificial way, but still working on it. I thought about sharing the results of this approach, just to show its pros and cons.

I haven’t tried what you are suggesting, I will check and comment you back soon, in a few days :-)