Vanity - Ebola model projects future case based on Daily Transmission Rate

Self | September 15, 2014 | Scouter

[scouter]

My User Name on Free Republic is Scouter. I have been a member of Free Republic for 14 years. I don't write many vanity posts, but I consider this one to be very important. I had been working on this post for several days, and I was planning to post it tomorrow. But the Drudge Report headline CDC: PREPARE FOR EBOLA has moved up my timeline.

I have developed a model for making future projections of the number of Ebola cases. I have undertaken this project for several reasons. First, out of simple professional curiosity. Second, I believe the time has come to be concerned and to prepare for the possibility that the Ebola epidemic could spread to other countries, including the United States. And third, my daughter will soon begin working as a nurse in a major Pediatric Intensive Care Unit, which will likely see some of the first Ebola cases in the United States, should it make an appearance here.

I am not an epidemiologist, and I have no inside knowledge about the current Ebola epidemic. But I have spent the last 26 years of my career applying computers to the practice of medicine and to medical data. I hold a Master's Degree in Medical Informatics from a major university known for their expertise in that field. I currently work in that field at a large, famous, metropolitan teaching hospital. I am remaining anonymous only because I don't want my employer to be held responsible for this post in any way. It is my work exclusively, and I am responsible for any information or projections it makes.

The numbers produced by this model are "projections", not "predictions". That is to say, I do not predict that there will be x number of Ebola cases on any given future date. Rather, I "project" into the future, assuming a constant Daily Transmission Rate (DTR), based on past data. Any number of factors can influence future DTR, in either a positive (bad) direction, or in a negative (good) direction. There is no way to know how these factors will actually play out. If there were, then we would be able to make actual preditions. As it is, we are left only with the ability to say "If Ebola continues to spread at the same rate it has been spreading for the past x number of days (or months), then this is approximately how many people who will have contracted the disease as of this particular date in the future." Not ideal, for sure, but still quite useful to understand the seriousness of the situation.

I have validated the model based on actual data by calculating the DTR for various periods of time and comparing the model's projections with what actually happened in subsequent periods. This is the same concept that is being used by epidemiologists at CDC and elsewhere. It is a valid method, within the constraints I have mentioned above. My model has been completely in line with projections I have seen quoted in the mainstream news. It works quite well. If anything, my model's projections are a bit more conservative than some projections you may have seen in the mainstream media. I just take them out further than you have seen in other places.

That being said, the following projections are based on the Daily Transmission Rate (DTR) from June 1 through September 10, the last date for which I have data. The DTR has remained relatively stable over that period. To be conservative I assumed that the reported number of cases represent the true size of the epidemic. However, the WHO, CDC, Medicins Sans Frontieres, and Samaritan's Purse all agree that the number of reported cases represents only 25% to 50% of the true number of cases. I have decided to be conservative in the numbers published below, but the model allows you to adjust this percentage.

As you review these projections, remember to pray for all those who are currently affected by this terrible disease, those who have it, those who will die, and their families. Do not forget that these are real people with eternal souls, who will either go to heaven or to hell, depending on whether or not they die in friendship with God. Pray, too, for an end to this epidemic. Do not underestimate the power of prayer!

The following projections assume that the currently reported cases represent 100% of the true epidemic size. In other words, that there are no cases that were missed by the epidemiologists. We know this not to be true, so we know that the "best case" is something worse than this, assuming the Daily Transmission Rate remains stable.

Scouter Ebola Projection Model Version 1.0 - Ebola Case Projections

*********************************************************
Projection Parameters
*********************************************************
Start Date: 6/1/2014
End Date: 9/10/2014
Reported cases represent 100% of the true epidemic size
Daily Transmission Rate (DTR): 1.00422415489918
*********************************************************

Weekly for the Next 8 Weeks

Date        Cases                 Deaths                Daily New Cases       Daily New Deaths      
==========  ====================  ====================  ====================  ====================
09/10/2014                 4,845                 2,376                   171                    84
09/17/2014                 6,227                 3,054                   219                   108
09/24/2014                 8,003                 3,925                   282                   138
10/01/2014                10,285                 5,044                   362                   178
10/08/2014                13,218                 6,482                   465                   228
10/15/2014                16,988                 8,331                   598                   293
10/22/2014                21,833                10,707                   769                   377
10/29/2014                28,060                13,761                   988                   485


End of Month for the Next Year from the End Date

Date        Cases                 Deaths                Daily New Cases       Daily New Deaths      
==========  ====================  ====================  ====================  ====================
09/30/2014                 9,923                 4,866                   349                   171
10/31/2014                30,146                14,783                 1,061                   521
11/30/2014                88,357                43,331                 3,111                 1,526
12/31/2014               268,427               131,637                 9,451                 4,635
01/31/2015               815,475               399,911                28,713                14,081
02/28/2015             2,224,815             1,091,055                78,336                38,416
03/31/2015             6,758,941             3,314,601               237,983               116,707
04/30/2015            19,810,535             9,715,135               697,531               342,071
05/31/2015            60,183,993            29,514,379             2,119,084             1,039,204
06/30/2015           176,399,989            86,506,991             6,211,061             3,045,920
07/31/2015           535,899,508           262,806,446            18,869,075             9,253,441
08/31/2015         1,628,051,594           798,400,534            57,323,860            28,111,763
09/10/2015         2,329,918,242         1,142,597,677            82,036,655            40,230,979

The following projections assume that the currently reported cases represent 75% of the true epidemic size. Remember that Medicins Sans Frontieres, Samaritan's Purse, the CDC, and WHO all agree that the number of reported cases already vastly underestimates the true size of the epidemic. They say by a factor of 2 to 4.

Scouter Ebola Projection Model Version 1.0 - Ebola Case Projections

*********************************************************
Projection Parameters
*********************************************************
Start Date: 6/1/2014
End Date: 9/10/2014
Reported cases represent 75% of the true epidemic size
Daily Transmission Rate (DTR): 1.00422415489918
*********************************************************

Weekly for the Next 8 Weeks

Date        Cases                 Deaths                Daily New Cases       Daily New Deaths      
==========  ====================  ====================  ====================  ====================
09/10/2014                 6,460                 2,376                   235                   115
09/17/2014                 8,373                 4,106                   305                   149
09/24/2014                10,853                 5,322                   395                   194
10/01/2014                14,068                 6,899                   512                   251
10/08/2014                18,234                 8,942                   663                   325
10/15/2014                23,635                11,591                   860                   422
10/22/2014                30,635                15,024                 1,115                   547
10/29/2014                39,709                19,473                 1,445                   708


End of Month for the Next Year from the End Date

Date        Cases                 Deaths                Daily New Cases       Daily New Deaths      
==========  ====================  ====================  ====================  ====================
09/30/2014                13,556                 6,648                   493                   242
10/31/2014                42,764                20,972                 1,556                   763
11/30/2014               129,996                63,750                 4,729                 2,319
12/31/2014               410,085               201,107                14,920                 7,317
01/31/2015             1,293,657               634,413                47,066                23,081
02/28/2015             3,651,570             1,790,739               132,851                65,150
03/31/2015            11,519,271             5,649,079               419,092               205,524
04/30/2015            35,016,714            17,172,283             1,273,972               624,759
05/31/2015           110,464,001            54,171,820             4,018,881             1,970,869
06/30/2015           335,792,614           164,673,529            12,216,744             5,991,122
07/31/2015         1,059,294,023           519,480,413            38,539,038            18,899,640
08/31/2015         3,341,657,268         1,638,757,001           121,575,553            59,620,953
09/10/2015         4,840,743,028         2,373,912,370           176,115,013            86,367,239

Obviously, there are many factors that will affect these projections. Rather, this model simply projects the number of cases and fatalities based on the current Daily Transmission Rate (DTR), which has been stable for about 3 months. Consider the following other factors that are likely to change the DTR (either for good or for bad) as we move forward from today:

1. Ebola is most easily contained in rural villages which can be easily quarantined.
2. The virus is already spreading in densely populated areas.
3. The virus is most successfully treated in hospitals, but hospitals in the affected areas are already overwhelmed, with Ebola patients already dying in the streets. This will clearly work to increase the Daily Transmission Rate.
4. On the other hand, as more and more aid is sent to West Africa, in the form of well trained personnel, equipment, and supplies, this will work to reduce the DTR.
5. As more people are educated how to avoid contracting and spreading the disease, this will work to decrease the DTR.
6. There are plenty of other factors, including the possibility of a vaccine, better treatment methods, better education, etc., that will influence the DTR over time.
7. The influence of weather on the DTR is unknown, but it is reasonable to assume that the weather will have both a direct and indirect impact on the DTR. The impact may be favorable in some effects, and unfavorable in others.

While the numbers quoted above are grim, they do not yet represent fact. Do not panic, but do not be complacent, either. Any preparations you make to "shelter in place" will serve you well for other contingencies, too.

On the other hand, epidemiologists are already saying that the number of cases is already doubling every two weeks. That means that the numbers I've posted above are actually quite conservative.

This model is contained within a macro-enabled Microsoft Excel 2010 spreadsheet (i.e., a .xlsm file). I would be willing to share it with other Freepers if someone can provide a place to post it for download and can tell me how to sanitize my name from it (again, I don't want my employer to be in any way held accountable for this).

[Axenolith]

1%, maybe even 1/10th%, of those Jan/Feb 2015 numbers being in western nations will probably seriously impact commerce.

LONG before any pandemic reaches the projection SHTF level in 2015 there will be economic ramifications that have major consequence.

[Smokin' Joe]

Ping...

A link to this thread has been posted on the Ebola Surveillance Thread

[trisham]

I fervently hope that you’re a complete whacko and totally wrong.

Thanks for posting, though.

[Tilted Irish Kilt]

Dallas59:" I wonder how many Chinese and Arabs fly to and from Africa?"

Better yet, consider the Hajj
Someone on the Ebola Surveillance board stated that there were 77,000 Nigerians scheduled to participate this year.
Authorities stated that they would be medically checked, but some are carriers who may not outwardly display any symptoms .

[Rockingham]

Yikes! Does your model assume the same rate of transmission in the developed world as in Africa? That would seem unlikely.

[taxcontrol]

The pale horseman rides.

“And when the Lamb broke the fourth seal, I heard the fourth living being say, ‘Come!’ And I looked up and saw a horse whose color was pale green like a corpse. And Death was the name of its rider, who was followed around by the grave. They were given authority over one-fourth of the earth, to kill with the sword and famine and disease and wild animals” (Revelation 6:7-8, NLT).

Up to 1/4th of the worlds population = 2 Billion.

[exDemMom]

Authorities stated that they would be medically checked, but some are carriers who may not outwardly display any symptoms .

Without symptoms, Ebola is not contagious.

Caveat: Unless you receive a blood transfusion from an asymptomatic case.

[grumpygresh]

I think it’s crazy that there are still flights out of East Africa to the rest of Africa, Europe, Mideast, and NA.
The virus has an incubation period of 2-22 days, so you can have asymptomatic carriers walking around with the disease for for 3weeks. There will also be the equivalent of Typhoid Mary cases that spread the disease.
The virus has been mutating to fast for effective vaccines.
Airborne spread is likely, and care givers need to wear at least P100 filters. Regular masks will not be adequate.
If this thing does go global, we will have medical martial law and the US government already has laws in place to do just that.

[babygene]

Wow

[RinaseaofDs]

Hi Scouter,

I’ve been tracking based on the WHO reported numbers. I have the new cases doubling about every 25 to 30 days.

Reason for using their numbers is that they are the most conservative available, and you can apply whatever scaling factor ends up emerging to correct the underreporting.

Do you generally confirm a doubling of 25 to 30 days?

I have around 6000 confirmed cases by around Oct 1, then 12K Nov1, 24K Dec1, based on the WHO’s numbers only - no correction factor.

[exDemMom]

Yikes! Does your model assume the same rate of transmission in the developed world as in Africa? That would seem unlikely.

Indeed.

AIDS spreads similarly to the way Ebola spreads (both are blood-borne pathogens). The majority of AIDs cases are in sub-Saharan Africa.

There is a HUGE difference between the US public health system and that of Africa.

[Jewbacca]

“This model is contained within a macro-enabled Microsoft Excel 2010 spreadsheet (i.e., a .xlsm file). I would be willing to share it with other Freepers if someone can provide a place to post it for download and can tell me how to sanitize my name from it (again, I don’t want my employer to be in any way held accountable for this).”

Print it, redact information.

Go copy it at Kinkis, scan it and post it.

[scouter]

I think yours is high. A month ago when the spread rate was 5% increase per day, I was projecting 200,000 in 90 days. But the most recent week showed a spread rate of 3% which would put us at 69,000 by Dec 12th. Basic formula that I’m using is: Current Cases * (SpreadRate)^#DaysOut)

I hope you're right. The formula I'm using is Cases ^ (((DTR-1) * DaysOut) + 1).

Let's do an example, based on the actual data:

On 6/1/14 there were 383 reported cases. 101 days later, on 9/10/14 there were 4,845 cases. This gives a DTR of 1.004224155. Let's see how that DTR would project from June 1 to June 30 (29 days later).

If you use the formula, you will get:

383^(((1.004224155 - 1) * 29) + 1)
383^((.004224155 * 101) + 1)
383^(0.426639655 + 1)
383^1.426639655 = 794

The actual number of cases on June 30 was 759. So it's about 5% high in this instance. But let's do it again using June's DTR to project what the number of cases were at the end July. June's DTR was 1.00396518542771.

383^(((1.00396518542771 - 1) * 60) + 1)
383^((.00396518542771 * 60) + 1)
383^(0.219111856626 + 1)
383^1.219111856626 = 1,410

But at the end of July (actually, July 30) there were, in fact, 1440 cases. So the model is pretty close, but comes in 2% low.

Keep in mind that the model will improve over time as the actual numbers are incorporated.

[familyop]

Thank you for the information. I would like to believe that it would spur nearly universal attention to good hygiene, but with the current paradigm of common thought and behavior, probably not.

[scouter]

Yikes! Does your model assume the same rate of transmission in the developed world as in Africa? That would seem unlikely.

Yes, it does. And that's one of the factors that will work to lower the projections over time. But while it's still almost exclusively in West Africa, the DTR may actually increase.

[21twelve]

“Does your model assume the same rate of transmission in the developed world as in Africa? That would seem unlikely.”

I have not heard a reasonable explanation why the “developed” world would have a lower rate of transmission. Better sanitation of course, but that sure doesn’t seem to prevent the transmission of the common cold.

Plus, in the developed world a sick person can travel to and from work (bus, train, elevator, etc.) and cover 20 miles in a day. A guy in some small village in Africa might travel 4 blocks in a week.

Our health care system is obviously better, but there are only a certain number of hospital beds. A quick search showed 10,000 in Minnesota. Maybe goes up to 50,000 with the National Guard, etc. setting up field hospitals. How many will still not be able to get treatment.

I would like to know what has stopped previous Ebola outbreaks in the past, when annual deaths were in the hundreds. I wonder if there is a certain number, or circumstance (such as the recent cases in large cities with international airports) where it becomes a “cat out of the bag” situation.

Prayers for those afflicted, and for those treating them.

[ElenaM]

Excellent analysis. Out of curiosity what CFR percentage did you use? It looks like 50%.

I can make your Excel sheet anonymous or tell you how to do it. Then upload the file to Scribd.com to share.

Thanks for the info. We in the Ebola Surveillance thread have been saying much the same for quite a while. Hearing it from someone in the coding/medical informatics field supports our admittedly less rigorous projections.

[scouter]

Print it, redact information. Go copy it at Kinkis, scan it and post it.

I was hoping to share the spreadsheet itself, as a working model, so others on Free Republic could critique the underlying assumptions, formulas, etc. There is embedded information in it that will identify me. Like I said, I don't want my employer to take the hit if I am, as another poster said, completely wacko.

[ElenaM]

Excellent analysis. Out of curiosity what CFR percentage did you use? It looks like 50%.

I can make your Excel sheet anonymous or tell you how to do it. Then upload the file to Scribd.com to share.

Thanks for the info. We in the Ebola Surveillance thread have been saying much the same for quite a while. Hearing it from someone in the coding/medical informatics field supports our admittedly less rigorous projections.

[scouter]

Out of curiosity what CFR percentage did you use? It looks like 50%.

I'm not sure what you mean be CFR percentage. I assumed that the reported numbers represent 100% of the actual epidemic. Does that answer your question?