Robert,

I have downloaded the DPLM.ZIP from the ftp. Thanks

Alan

Robert,

I am interested in lognormal double Pareto distribution to be used for Stock trading. Can you share the associated Mathematica package.

Alan

Yes, of course, that linear behavior we currently see cannot go on forever: At the very least, once we're getting closer to 100% of the population infected things will have to asymptote.

However, at this point, even taking into account that the number of people infected may be an order of magnitude higher than what the number of known (=tested) positives imply -- currently at about 1.4M, so ten times that number makes 14M -- we currently have only a few percent of the population infected.

The picture I have in my mind, from the remark in my previous post, is one of an "infection front" spatially moving through the population at constant speed, which may produce the linear growth in case numbers we are seeing now. This may go on like this for another couple of months. On the other hand, the good news is that the behavior is linear, thus the number of new cases per day is constant, and if things remain that way they will remain manageable.

What is somewhat interesting about this fit is that it's been fairly stable for more than a month now (use the slider in the dynamic plots to see how the fit has been changing over time as more data has become available). I do wonder if we can find a plausible model that would generate this kind of distribution. I vaguely remember from many years back obtaining similar behavior when I was working on hyperbolic one-D transport-reaction equations that we had obtained for fixed-bed absorption/desorption processes.

I was specifically thinking of this article/post. Some interesting ideas there, but you'll have to run this on some fairly high-powered cluster to be able to study networks and parameter sets large enough to start providing guidance for the real word.

Robert, I found the paper you forwarded interesting, at first blush. I'll take the time to explore it well. Thank you! Brian W

About that step change in Deaths: I notice Worldometers updated US DEATHS about an hour ago - local time, actually 04:17 GMT tomorrow! Here's what that one and only decaying plot looks like now: Their usual update happens around noon. Looks like that double exponential may go back to its former linear growth....

Brian W

Brian,

Just clicked on the link, they are now reporting 45318, deaths for 4/22. I don't know how often they update, but it eventually may be showing up there as well. Are you analyzing with Mathematica?
We are getting to an interesting point in the epidemic, which should decide the fate of the logistic model. The logistic model requires an exponential decline, which is easiest to show in the log plot of the daily differences.

In the picture the orange dots are the daily differences of the raw data and the curve is the calculated daily difference from the logistic fit to the cumulative data as a continuous curve which is very close to the first derivative curve. If the points don't follow something close to a log linear decline, I don't think the logistic model holds, but with data anomalies it may be difficult to track. I am finding that the death data is lagging the case data by 7 to 8 days. In the end the death data may be more reliable, especially if people start reporting antibody tests as positive cases.

Bob

US Data going the wrong way?

I just updated the notebook I posted with the latest data. This does not look good. Looks like the United States is turning the corner, the wrong way…

On your last remark, yes, that is the issue with trying to predict the future: It's really hard to do in advance; it's much easier to "predict" (=explain) the future once it's not the future anymore, but that's not as helpful in our current situation. This is also the difficulty with those SIR/SEIR/etc. "first-principle" models. They are really pretty, and work alright once all the parameters are known with sufficient accuracy. Unfortunately it turns out that we typically have a good grasp of those parameters only after the epidemic is over.

Oh dear. This model seems to be using RATE information as its source - which leads to the usual problems with noisy inputs.