4/24/2020 Welcome to Dan's Coronovirus Blog. Today's topic is the IHME Model.
I do not understand how the IHME model works. Apparently this is an ongoing problem. A 2018 Korean paper (Biomed Res Int. 2018; 2018: 7236194) comparing IHME and WHO models contains this statement: Despite the in-depth review, there was “black box” <calculations-DB> that could not be explained specifically. IHME statements described "Gaussian fits". The problem is that mathematical distribution functions have no direct first principle design in growth. The correct math is X=X0e^ut where X=cases now Xo=starting cases u=growth rate (Mu) and t=time. The spread of infection mimics microbial growth. There is no support or the idea that the "growth" of infections shape should impact the "extinction" of infections shape other than the magnitude of total numbers prior to the retreat in daily number of cases. That is, the downcurve of cases is likely to be much slower than the upcurve, especially in a more open society where extreme Wuhan style lockdown is unlikely. If anyone has connection with IHME I am basically calling their whole model into doubt. Their expectation is cases to drop very low (10s per day) by June 1. I don't see anyway that happens. (And yes they have a confidence range but that value is NOT being used in any news or decision maker reporting). My model is built on the exponential equation. I did flip things to be a daily multiplier to get rid of the exponential equation to make it more accessible for folks without comfort with e math. I call that daily multiplier Rd (credit to tweets by Robert Williams @ifsBob). If there are 100 cases today and the multiplier is 1.3, then tomorrow there are 130 cases. That simple. Rest assured the exponential math is still there Ln(Rd)=u. I used Rd of 1.3 for rapid spread and 1.1 for initial social distancing. These were empirically determined from US data. I then looked to Italy and used 1.0 for a plateau period and 0.97 for the extinction term. Note that .97 per day works out to 0.8 for the week. Also, I am estimating Rt (effective transmission ratio) by Rd^5.6 with 5.6 days being the average transmission interval (CDC). Rd of 0.97 gives an Rt of 0.84. *Much more goes into the formal calc. I am at best a hobby epidemiologist--I've read several books on history of disease, but I did NOT stay at a holiday inn express last night). Note my model is not built on a calculated basis of efficiency of transmission, number of people encountered by an infected person, etc. Rather it is based on readily observable net rates from the US data and from Italy, which seems to be a good comparable for growth and extinction. From there I simply sum positives. To estimate deaths, I found a simple correlation that -7 days positives x 00.7=today's deaths. Since I started, IHME has added "Exponential splines" to their curves and a -8 day positive to death correlation term. On the chart are the days I adjusted Rd. Since I did this early April, the 1.3 and 1.1 were determined empirically (I did not predict them), from there I essentially eyballed Italy and made my own approximation for timing and magnitude of the multipliers as spread was slowed. Its been over two weeks now and I have not touched a thing. Please note my dates are when behavior changes show up, not the data of government policy changes. All data is from Covidtracking.com. To remain as a good quarantine partner to my fantastic spouse, I have not done much on a state by state basis. If I do too much of this I get quite cranky. I screamed at Lester Holt about the IHME model the other day. He did not even look up at me as he just continued to read the news).
1 Comment
Dan Beacom
4/24/2020 07:58:52 am
Testing the comments section. Please keep it on topic and reasonable. While I have political opinions on this subject I will strive to keep this blog about data and solutions to the Covid crisis. With the one caveat that lives>>>>>>money for me. I am personally at essentially 0 income as my clients have mostly shut down for the time being. Stay alive today. Recover tomorrow. Vote for those that will help make that happen, however you think is best. Thank you.
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Dan is a consulting in fermentation Microbiology. On this Blog are my personal thoughts on the current covid crisis as a companion to my LinkedIn posts. Please checkout the rest of this site. Contact me if you have any question or comments. |