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

In the US and other developed countries, there are well-established public health measures to identify, isolate, and treat dangerous infectious disease cases and contacts. This would probably suffice for even Ebola, but, if not, the menace of a general outbreak would swiftly lead to stronger measures such as the cancellation of public events and suspension of non-essential work, shopping, and travel.

A co-worker told me of a case where a man fell ill after traveling, and was admitted to the hospital and died without diagnosis. Because of routine infection control measures, no one else got sick. A year later, analysis of stored samples revealed that he had Marburg.

I'm sure that you are aware that Marburg is another filovirus, and is almost identical to Ebola in disease characteristics.

Fun bit of history: Marburg was first identified because of an outbreak in Marburg, Germany, after it was imported by a traveler. Unlike all of these doomsday scenarios so popular with the conspiracy-theorists, this importation did not spread around the world and kill off 80% of the population--it was quickly contained there in Marburg. That was achieved because of routine infection control measures, nothing else--the medical staff had no clue what the disease was.

I appreciate the presence of another logical voice on the forum. The doomsday scenarios need to be countered with facts--spreading falsities about the disease might be amusing to the conspiracy-minded, but it only makes the situation worse.

I, for one, will be glad when people finally get bored with Ebola and it fades into the background again.

I meant to say, I don’t think there are new cases in Nigeria. There are certainly new cases in the other countries.

Oops, I should have fact-checked before hitting the “post” button. The Marburg virus was imported into Germany in an African green monkey. Laboratory workers first became ill. Altogether, 31 people became ill and 7 died. And the virus never spread beyond that initial outbreak.

Marburg spreads the same way as Ebola.

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The Lassa Fever virus is another hemorrhagic pathogen that causes about half a million cases per year in West Africa. About 80% of those infections though are asymptomatic, but there also some 5,000 deaths from Lassa virus every year, commonly with high fever and hemorrhagic symptoms.

In the 1970s, especially virulent outbreaks of Lassa Fever caused a panic similar to that which now attends popular discussions of Ebola. Today though, supportive measures and antiviral drugs are effective enough that 75% or more of even those hospitalized due to severe Lassa fever infections survive. US Army researchers also have a promising vaccine candidate on the verge of human trials.

My guess is that is where we will be with Ebola in a decade or so: no major outbreaks in the developed world, and with Africa beginning to benefit from treatments and vaccines that the US and Europe have developed, just as has happened with the Lassa Fever and Marburg viruses.

AMEN

The most important way is in the way we treat the dead. We don't wash the bodies, we don't give them enemas. Instead, we ship them off to a mortuary to prepare for burial or cremation. During the funeral, most people do not touch the body. This is very different than the African burial customs which are completely responsible for the early spread of Ebola. Later on, nocosomial infection became important.

My brother-in-law recently died from a short battle with cancer at home. While he was dying he was kissed and hugged repeatedly by his wife, kids and grandkids. They knew he was dying and they were saying goodbye.

People aren't robots. When someone is dying at home of Ebola they're not going to gown up. They're not going to refrain from kissing and hugging them out of love and compassion. That's exactly what's happening there. That's part of the "culture" that we have over here.

That’s just appalling. This country has been damned by the liberals and their immigration programs.

In the US and other developed countries, there are well-established public health measures to identify, isolate, and treat dangerous infectious disease cases and contacts.

Sure. So with the very real chance that Ebola could show up here any time how many doctors are fully suiting up to examine each and every patient who comes in with flu-like symptoms? The hard truth is that most medical professionals have never had to fully suitup for anything because the worst that could happen is that they pick up a cold or a flu. With Ebola, the worst that can happen is they die.

This would probably suffice for even Ebola, but, if not, the menace of a general outbreak would swiftly lead to stronger measures such as the cancellation of public events and suspension of non-essential work, shopping, and travel

Under penalty of what? I'm going to bet that the first time someone tells the residents of Ferguson (or any other black community) that they have to "stay home" some politician is going to pull the race card. This might have once worked in a United States where people respected law, order and the government. But our "leaders" have been very diligent to insure that hardly anyone holds these values.

An outbreak of Ebola in a developed country would lead to face masks, gloves, and the general spraying of disinfectant becoming routine in public places. In contrast, in Africa, poverty, corruption, theft, and the shambolic nature of its societies commonly make it impossible for even medical personnel who treat Ebola to have the benefit of containment garments and disinfectants.

Again I think you have an idealized version of the US in your head...possibly based on where you live. Look at the reaction of certain people to Katrina. Look at inner cities. Look at any large city for that matter. Many of the residents and officials are just as ignorant, just as corrupt, just as dishonest. If this disease takes hold in a black community you can bet that it's going to be billed as a racist plot by whitey. One of the problems in Africa was that many thought that Ebola was fake...that they were really just trying to get blood from people. Have large groups of people in this country ever been convinced of something that isn't true? Trayvon Martin? Saint Mike?

In a developed country that suffered an Ebola outbreak, medical care for the disease would improve rapidly, with new treatments and vaccines fast tracked into use. The result would almost certainly be the rapid and permanent containment of any such Ebola outbreak, just as bird flu and SARS were contained despite the dire predictions that attached to them.

Bird flu does not and cannot spread from person to person. You could only get it from direct contact with an infected bird. SARS isn't news anymore but it really wasn't contained. It ripped through several countries. And death from it was primarily in old people. There are and were people in the United States that have likely had SARs and just chalked it up to a bad flu or cold. How many times has something been "going around".

Ebola aren't like these. The Zaire strain has an up to 90% kill rate. Young, old, doesn't matter. It spreads person to person relatively easily in almost the same way SARS does.

In sum, Ebola is cause for concern and excitement in the US and other developed countries but is extremely unlikely to generate more than a relatively small number of cases.

Based on what? That's exactly what they said about it in Africa. Until is showed up in populous places. Once it shows up in a population all theories and practices about containment become kind of cute. Part of the effort is to trace back the activities of victims to see who they might have infected. This works up to a certain point. But it doesn't take much to overwhelm whomever's "job" it is to do this. Take any one hundred people in a mobile society like the United States and try to compile of list of everyone they might have come into contact with in the past week. Did anyone of them go to sporting event? Get on the subway?

Have you read "The Hot Zone"? It's not fiction. It is a detailed account of the major ebola outbreaks up until the mid 90's. Read it free here.

Ebola is the worst nightmare of virologists. Read it and see why.

God is a bit angry. Has the right.

Your math is not making sense to me. First a DTR (Daily Transmission Rate) of 1.004 is way too low. And I’m not sure what you are doing putting both the DTR and the DaysOut in the exponent. That might work in your formula, but I don’t think the formula makes logical sense. Start with 100 cases and let’s do just 3 days. If you have 100 cases on day 0 and the DTR is 1.004 then you would have 100*1.004 = 100.4 on day 1, and 100.4x 1.004 = 100.8 on day 2, and 101.2 on day 3.

Excellent Question!!!

I think part of the problem is that I call it a Daily Transmission Rate. I chose a bad name for it. It's not really a rate in the sense we're used to, e.g., "rate of speed", where you have "miles per hour", or "new cases per day". Rather, it's really a rate of increase in the rate of new cases per day. In other words, it's a measure of acceleration of transmission, based on the fact that as the number of patients increases each day, there will be correspondingly more patients infected by them.

Using a true "rate", we would say, for example, that "each day there are 10 new cases of Ebola". So if there are 100 cases on Day 0, then on Day 1 there will be 110 cases, and on Day 2 there will be 120 cases, and on Day 3 there will be 130 cases. Every day we would simply add 10 new cases to the total.

But that's not the way it works. In addition to each of the 100 cases on Day 0, each new case also becomes capable of transmitting Ebola. Therefore, to project into the future, we need to measure how many cases there will be on Day 2, given that there are 110 cases on day one. Or, to put it another way, given that 100 cases became 110 cases on Day 1, how many cases will 110 cases become on Day 2? It's kind of like compounded interest.

But wait... it gets even more complicated. In most diseases, once a person recovers or dies, they no longer transmit the disease. So some of those original 100 are no longer able to infect others. So the question becomes "given that 100 cases became 110 cases on Day 1, and that some unknown number of those original 100 are no longer infectious, how many cases will 110 cases become on Day 2?"

But wait... there's more... With Ebola, even those who have recovered or died can transmit the disease.

But wait... there's even more... Those who have recovered, and those who have died can only transmit the disease under certain circumstances, and for each circumstance, there is both a different transmission rate, and a different length of time they can transmit it.

To go back to the compounded interest analogy, it's kind of like saying "How much money will I have in 90 days if I start with $100, but x dollars don't generate any interest, xx dollars generate interest at yy APR, for zz days, and and xxx dollars generate interest at yyy APR for zzz days, and I don't know what the values of x, xx, yy, zz, xxx, yyy, zzz are?"

So you see it gets very complicated very quickly. So to simplify all of this, my model looks at what actually happened over a period of time to calculate a rate of increase in the transmission rate (the DTR), from day to day. Because it is based on what actually happened, it takes all those factors described above into account, as well as the effect of the weather, the number of people per acre, the effect of quarantine and treatment, the deaths of healthcare workers, and on and on, including factors we would never think of.

So the question gets reduced to this: What exponent can I put on the number of cases, such that, if I apply it x number of times, will estimate the number of cases I can expect to see after x number of days?

The Microsoft Excel formula for the exponent is: (LOG(EndingCases,StartingCases)-1)/DaysOut + 1, where EndingCases is the number of cases at the end of the time period being considered, StartingCases is the number of cases at the start of the same period, and DaysOut is the number days in the period. I call this exponent, somewhat inaccurately, the Daily Transmission Rate (DTR).

The DTR measures the rate of increase in the rate of transmission over a previous, known period of time. To project into the future, I apply the DTR in the formula: FutureCases "X" Days from Now = CasesToday^(((DTR-1) * X) + 1).

But wait... there's still more... The DTR fluctuates, depending on the specific StartDate and EndDate examined. And even a small fluctuation can alter the projections dramatically. So, to minmize the fluctuations, I chose a period of time where the DTR was fairly stable over a significant period of time. That time period is June 1 through September 10.

The rates of transmission and fatality for Ebola in backward and struggling Africa cannot be taken as applicable to developed countries with modern health care and standards of living.

In the US and other developed countries, a tangible and immediate threat of Ebola infection would quickly induce medical professionals to become acquainted with and to follow the necessary protocols. Similarly, the public would voluntarily avoid going out from their homes for non-essential tasks.

The authorities would avoid confrontations with and discontent by the public by turning a medical crisis into an enjoyable stay at home holiday. Simple measures would work the trick: delivering free food and household supplies door to door using the National Guard; upgrading and providing free cable; putting first run movies on broadcast and cable; shutting down most gas stations and common carriers; and closing schools and nonessential forms of employment while providing for continued salary and wages.

Several weeks of that would break the chain of transmission and would permit existing Ebola cases to be identified, isolated, and treated. Thanks for the link to "The Hot Zone."

Congrats, Scouter. Your model has been noticed by Gateway Pundit.

Research Model Projects 1.1 Million to 2.3 Million Ebola Deaths By September 2015

Given your qualifications for creating these projections, as to the qualifiers effecting the data as it unfolds in the real world, in your work with statistics are their not certain logarithmic formulae that can be applied, particularly with the data when the available pool becomes larger and perhaps more accurate, that might tighten your projections around probabilities? Wouldn't it be more accurate to hash out columns rated against their range of probabilities, e.g., 10-20 % 10 to 20 millions; 20-30 % 10 to 5 millions, etc?

Just to clarify my statement about my background... I am neither an epidemiologist nor a statistician. Although both disciplines were part of the curriculum in Medical Informatics, they were presented in more of a "Statistics for Dummies" kind of way than as a major component of the degree. Medical Informatics centers more around the application of computers to the daily practice of medicine and to medical information.

That being said, you bring up an interesting point. At some point, the number of people in the susceptible population will be reduced to the point where the rate of increase in the transmission rate (what I call, somewhat inaccurately, the DTR), will start to fall, even to the point where it decelerates instead of accelerates. I do not believe that on September 10, 2015, there will have been 2,329,918,242 cases, as the model projects. Precisely for this reason, if for no other. This is why I was so emphatic that these are projections, not predictions. They simply say "If we take the current rate of increase in the rate of transmission and project out 1 year from September 10, 2015, and if nothing changes between now and then (including the size of the susceptible population), then there will be approximately 2,329,918,242 case by then." Of course, it won't work out that way. But it is helpful for short term projections and to indicate the seriousness of the epidemic.

Unfortunately, I don't know how to calculate the range of probabilities you mention, or how to incorporate the effect of the decrease in the susceptible population that will occur as the epidemic develops. I would welcome that kind of assistance from someone who can offer it.

Congrats, Scouter. Your model has been noticed by Gateway Pundit.

Precisely why I wanted to remain anonymous!

Please, anyone reading this, understand that the model is the work of a knowledgeable amateur. Nothing more. Go back and read all my posts on this thread, especially the ones that explain the model's limitations and how it works (posts 111 and 114), along with the ones where I emphasize that I do not believe there will be as many cases or deaths as projected by this model.

Also, please note that I am neither an epidemiologist nor a statistician, and I have not presented myself as one. I am a computer programmer with 26 years of experience applying computers to medicine and medical information, with a Master's Degree in Medical Informatics.

This post was intended only for discussion and critique by other members of Free Republic. The model I developed is not in any way suitable for publication in a peer-reviewed journal.

I'm not backing off anything I've said. I'm just trying to put it in its proper context so that people don't flip out.

Okay, implicit in the way I was using a DTR is the assumption that the rate of death and recovery is built into the DTR and that those rates will remain constant so that spread rate will also remain constant.

But I understand what you are saying. I'm just not convinced yet that the math is right. And I think it's best to start with a day to day formula instead of starting with what exponent we can apply. And then once the day to day formula is developed, work into the exponent.

If your DTR is actually measuring the acceleration of the rate of transmission, given the current slope, and the nature of the disease, I'm not sure what I would predict acceleration doing in the future. The chart is definitely a curve right now and showing acceleration, whereas my formula assumes a constant rate of transmission and thus a linear progression.

But I think I'd prefer to project using a constant transmission rate with no acceleration. I'm not sure what factors would cause it to continue to accelerate.

Plus I'm not comfortable with seeing an acceleration rate in your formula but not an initial transmission rate. That makes me think your formula assumes that the initial spread rate in any projection period is 0 and accelerates from a speed of 0 each time. I'm thinking here of dropping a ball from a building. It starts at 0 and has a constant acceleration to a point. But our Ebolaball is already on the move.

In any event, it appears that my flat rate went from 5% to 3% so I think it's deaccelerating to some extent, though the slope is still insanely scary.

if we knew the missing values, We could expand the formula for Active Cases on Day1 from:
Day1 = Day0*DTR
to:
Day1 = Day0*DTR-ResolvedCases+NewCasesFromResolvedCases
Where
Resolved Cases = Dead_Day1 + Cured_Day1
NewCasesFromResolvedCases = ContagiousDead * ContDead_DTR + Cured * Cured_DTR

But we don't know those numbers.

During the SARS episode, someone had a model of how diseases would spread over the earth, given traffic patterns. I wish I could find that.

Okay, implicit in the way I was using a DTR is the assumption that the rate of death and recovery is built into the DTR and that those rates will remain constant so that spread rate will also remain constant.

But I understand what you are saying. I'm just not convinced yet that the math is right. And I think it's best to start with a day to day formula instead of starting with what exponent we can apply. And then once the day to day formula is developed, work into the exponent.

If your DTR is actually measuring the acceleration of the rate of transmission, given the current slope, and the nature of the disease, I'm not sure how I would predict acceleration in the future. The chart is definitely a curve right now and showing acceleration, whereas my formula assumes a constant rate of transmission and thus a linear progression. I simply pick recent points to calculate the DTR, so I'm picking up the current slope.

But I think I'd prefer to project using a constant transmission rate with no acceleration. I'm not sure what factors would cause it to continue to accelerate.

Plus I'm not comfortable with seeing an acceleration rate in your formula but not an initial transmission rate. That makes me think your formula assumes that the initial spread rate in any projection period is 0 and accelerates from a speed of 0 each time. I'm thinking here of dropping a ball from a building. It starts at 0 and has a constant acceleration to a point. But our Ebolaball is already on the move.

In any event, it appears that my flat rate went from 5% to 3% so I think it's deaccelerating to some extent, though the slope is still insanely scary.

if we knew the missing values, We could expand the formula for Active Cases on Day1 from:
Day1 = Day0*DTR
to:
Day1 = Day0*DTR-ResolvedCases+NewCasesFromResolvedCases
Where
Resolved Cases = Dead_Day1 + Cured_Day1
NewCasesFromResolvedCases = ContagiousDead * ContDead_DTR + Cured * Cured_DTR

But we don't know those numbers.

During the SARS episode, someone had a model of how diseases would spread over the earth, given traffic patterns. I wish I could find that.

But I understand what you are saying. I'm just not convinced yet that the math is right. And I think it's best to start with a day to day formula instead of starting with what exponent we can apply. And then once the day to day formula is developed, work into the exponent. (emphasis mine)

That's how I did it. I looked at various time frames and asked "How do we get from this number to that number in so many days?". There are really two complementary pieces to the model: 1) how to calculate the exponent from specific past periods of time; and 2) how to apply that calculated exponent to the future.

I like your terminology of "resolved cases".

But I think I'd prefer to project using a constant transmission rate with no acceleration. I'm not sure what factors would cause it to continue to accelerate.

The point of this whole exercise is to get at the truth. No one model will do that. We need multiple models that look at the problem from various points of view, all of which are imperfect, but each of which reveals something the others don't.

In any event, it appears that my flat rate went from 5% to 3% so I think it's deaccelerating to some extent, though the slope is still insanely scary.

I have noticed a deacceleration of my DTR, too. That's a good thing and will dramatically lower the projections in my model. But like yours, my numbers are still pretty scary.

If your DTR is actually measuring the acceleration of the rate of transmission, given the current slope, and the nature of the disease, I'm not sure how I would predict acceleration in the future.

In college, back in the 1970's, I had a professor of Effective Writing (i.e., Freshman Comp) who told us that "Language is Thought", and if you don't know how to express something clearly, it is because the thought isn't clear in your own mind. This discussion is really helping me clarify my own thinking on the matter.

The more I think about what my DTR really represents, the more I don't like how I've said it. I'm not sure I like the word "acceleration" as I've used it and as others are likely to understand it. I know I don't like the word "rate". It's not a "rate". It is a "rate of change".

So let's try this: the DTR in my model should be renamed "Adjusted Transmission Exponent (ATE)". It is an alternative way of expressing the rate of transmission, adjusted for the variations that have occured over time in the rate of transmission, both positive and negative. It "smooths out" the daily, weekly, and monthly variations in the rate of transmission to provide a single number that can be used as a mathematical exponent to project into the future, based on past transmission rates.

Glad I’m helping.

I’m still not sure that your exponent represents what you want it to represent. It seems to work. The projection 3 months out, is reasonable for a model that includes a positive increase to the rate of change. but without a clear understanding of what it represents, I’m not sure when you go out beyond 3 months that it’s still a valid model.

Try this. Try to express it as a simple day to day formula formula without exponents. Day1 = Day0*whatever+/-whatelse. If you can do that, we can test to see if the exponent formula is correct.