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Re: [stem-dev] Operon Ebola Models Available
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Hello Dr. Althaus,
Glad to hear from you, and thank you for taking the time to review my
model. I posted the B2 version, although I have gone through a number
of iterations of the model with many different parameters.
The USA model was a 'thought experiment' extrapolated from my West
Africa model.
In my opinion, it is not very sensible to simulate a hypothetical
outbreak of Ebola in the US, assuming that all parameters are the same
as in West Africa
Agreed that a hypothetical outbreak in the US would have different
parameters, especially if top-notch resources are able to respond, and
the CDC's response capability is strong. My model doesn't represent the
'current' situation in the United States or even a 'near future'
situation in the U.S.. The model is based on the hypothetical question
of 'What happens if there is an abject failure to contain the disease in
West Africa'?
I say this because there is the possibility we go from hundreds of
causes per week in West Africa to thousands of cases per week or more
(according what I am reading on ProMED-EDR). . . This would mean the
disease could continue to outpace the response through the end of 2014.
I agree my current USA 'B2' worst-case scenario model definitely needs
revisions to the parameters, as you have kindly pointed out in your
analysis. I will be revising and re-releasing all the Operon models
starting next week.
I do think the USA simulation is useful idea to capture a 'worst-case'
scenario -- meaning a global pandemic. The model was based on the
following assumptions... that the Ebola virus is (1) not contained in
West Africa, (2) eventually takes hold in Nigeria and other rich African
countries, then (3) moves into Western countries including the US.
Here are two 'narratives' of a best-case and worst-case scenario in the
global Ebola outbreak. My goal is to create STEM Ebola models for
best-case, worst-case, and most probable-case scenarios.
Best Case Scenario Narrative:
"WHO immediately deploys contact-tracing teams on the ground in West
Africa. The US Military is deployed as well, and constructs hospitals
sufficient to care for the sick. The hospitals are staffed by qualified
(read: well trained) caregivers. Teams on the ground track down and
care for Ebola-infected patients across West Africa, distributing
self-treatment kits, food, medicine, and expertise. An effort is made
to involve local authorities and community leaders. These efforts cause
measurable reductions in the basic reproduction number of the virus by
the end of 2014.
Within 3 months to 9 months, the outbreak in West Africa peaks,
levels-off, and begin to fade. The Ebola virus never has the
opportunity to acquire any significant mutations, due to its limited
host pool. Ebola is fully under control by early-to-mid 2015. Sporadic
cases in other countries are dealt with by treatment and contact
tracing. By Q4 2015, multiple Ebola vaccines and drugs are in the
pipeline limiting the overall threat Ebola poses."
Worst-case Scenario Narrative:
"By Q1 2015 the number of infections is in the hundreds of thousands in
West Africa. The West African region exports asymptomatic carriers which
go undetected by basic Customs screening. Export of asymptomatic
carriers into the U.S. keeps seeding new clusters of disease within
cities across U.S., each which require large deployments of resources to
contain.
The repeated import of Ebola clusters from Africa and other regions
begin to saturate the US's logistical, medical, and contact-tracing
capabilities (CDC, HHS, and state DOHs). Ebola patients begin to slip
through the cracks... They are discharged with incorrect diagnosis
during flu season, and travel freely in the community during their
incubation and early infectious periods. The uninsured urban and rural
poor are at high risk for undetected or misdiagnosed disease in general,
as they are likely to avoid medical treatment at all due to high cost.
Several months after repeated import of clusters stretch US response
capabilities, the ability to respond becomes saturated. Contact tracing
may not be possible for all potential exposures. Hospitals see
increasing stream of panicked self-diagnosed 'Ebola cases' which have no
travel history to WAfrica. (This is already happening now) These
'worried well' mask actual sick patients with Ebola presenting to
hospitals. There only four BSL4 units in the U.S., so any substantial
number of Ebola cases will need to be handled in either community
hospitals or in designated treatment centers.
Hospitals then have trouble differentiating between real Ebola cases,
the 'worried well', or other diseases like Influenza -- since PCR
confirmation tests will not show positive until 1 to 3 days after Ebola
symptom onset. The limited number of Ebola testing labs become
backlogged from the daily testing load. At a certain point, if (1) US
is importing asymptomatic carriers on a weekly basis, (2) US
contact-tracing capability response remains saturated, and (3) Hospital
case-detection and infection control procedures are not sufficient (like
the recent situation in Dallas)... Then uncontrolled community spread
could become a real threat (as more and more Ebola patients appear in
the community, outside hospitals). After a certain 'critical mass' of
Ebola cases in the US (perhaps 100,000 or more), the spread of the virus
in the US could be beyond traditional response efforts. "
<end of 'worst-case' scenario description>
<-- This is what I was trying to model in the US. . . "What is the
worst-possible outcome? What is the 'black swan' event here?" rather
than "What is the most probable scenario?".
I do agree that the worst-possible outcome is very unlikely, especially
if all the WHO roadmap milestones are reached on-time and as promised...
Meaning a very strong international response is in place in West Africa
by Dec 31 2014.
I think it is just too early to tell exactly how this will play out... I
don't think we have enough data to say 'Everything is fine and will
remain fine', nor do we have enough data to say 'The will result in
millions of cases'... My opinion is that the outcome primarily depends
on what happens in West Africa between now and Q1 2015.
My instinct is that we will have a much better understanding of the
situation as we approach Jan and Feb 2015 , when we can look at the
outcomes in Guinea, Sierra Leone, Liberia, Nigeria, and Senegal. Then
we will know if this is a 'big deal', a 'false alarm', or most
hopefully, a historical example of excellent international health
coordination.
The USA model was built to ask 'what could the most problematic
situation look like?'
as in West Africa. The R0 of Ebola in the US and other western
countries would clearly be lower, most likely below 1. That means,
that any import of cases could only cause a small outbreak as seen in
Nigeria for example.
Nigeria seems to have done a great job so far. I found it especially
impressive.. The Nigerian response was able to contact trace and deal
with several hundred people, all caused by Patrick Sawyer. But I wonder
what would happen if Nigeria had to contact trace 100x or 1000x more
people? What if Nigeria repeatedly imported Ebola cases over their land
border ? Could they handle it? Suppose Ebola were to become widespread
in Lagos... what would happen to the R0? I don't know the answer.
I think that a large scale outbreak in the U.S. is unlikely (almost
impossible) if West Africa is properly contained soon.
My STEM model in the U.S. is predicated on a _failure_ to control the
Ebola outbreak in Africa. If cases reach hundreds of thousands in W
Africa by Q1 2015, then I think there will also be substantial spread to
rich African countries like Nigeria, into population-dense cities like
Lagos, and eventually to Western countries. Hopefully that doesn't
happen, and I think we are fortunate that such a scenario is very
unlikely.
But I still wanted to model a worst-case Ebola scenario in the US, as an
example of a 'Black Swan Event'...
[Black Swan Theory] was developed by Nassim Nicholas Taleb to explain:
1. The disproportionate role of high-profile, hard-to-predict, and rare
events that are beyond the realm of normal expectations in history,
science, finance, and technology.
2. The non-computability of the probability of the consequential rare
events using scientific methods (owing to the very nature of small
probabilities).
3. The psychological biases that make people individually and
collectively blind to uncertainty and unaware of the massive role of the
rare event in historical affairs.
http://en.wikipedia.org/wiki/Black_swan_theory
The doubling time of a simulated epidemic is determined by your
assumed values of R0 and the average generation time. So it's no
surprise that the doubling time you observe is similar to the one in
West Africa. You could easily calculate the doubling time from your
formulas.
Part of what I did was evaluate how STEM's 'add stochastic noise' and
'frequency-dependent vs density-dependent' parameters effected the
recorded output parameters (like doubling time). You are 100% correct
that the doubling-time is more or less determined from the input
parameters. But since I was new to STEM, I wanted to see for myself , to
see what parameters were sensitive to initial conditions, to
double-check and validate all my input and output parameters and ensure
they were within expectations... Especially since my Delta (death-rate)
parameter was 'reverse engineered', so to speak.
I don't think that the infectivity period is the same as the interval
from symptom onset to hospital discharge. People who are discharged
will not have been infectious for at least a few days. From the WHO
paper, I think it is better to look at the interval from symptom onset
to hospitalization (5 days) or death (7.5 days). Alternatively, you
can calculate the infectious duration as the difference between the
serial interval (generation time) and the incubation period, i.e.,
15.3 days - 11.4 days = 3.9 days. Remember that in your model you want
to know the time during which people do transmit, and not the time
during which they could transmit. If people are hospitalized quickly
and there is not much transmission in the hospital, that means that
the infectious duration can become shorter.
Thank you for your thoughts on this... this is extremely helpful
commentary. This has been a critical question I have had for over a
month now.
The Ebola SEIR infectivity period has been a point of discussion for
some time . . . Caitlin and I had discussed which numbers to use about a
week ago, as she has more expertise in epidemiology than do I.
Originally I was using the time from symptom onset to death (but this
reduced the outbreak doubling time below the observed values). In
simulation B2, I decided to change to use the time from onset of
symptoms to hospital discharge, though that value seems like it is a bit
too large.
Thanks for the tip on using the serial interval / incubation period
difference... The only problem is that I don't think the mean infectious
duration of EVD is 3.9 days... That seems to short. I may revert back
to using the time from symptom onset to death (7.5 days), then go back
and check all the numbers again after implementing the fixes you have
suggested.
Also, in the model, I wanted to assume that transmission in hospitals is
identical to that in communities... especially considering that whole
incident in Dallas with Duncan infecting the two other health care
workers. Hopefully that was just a fluke, not the norm.
But I do agree, under rigorous conditions and proper protocols, then
when someone enters a hospital with good infection control, they should
be no longer transmitting disease in the 'community' as defined in the
model.
Kun has made a model with an explicit hospital and funeral compartments
that would be much more useful than my generic SEIR model. Perhaps we
should try deploying her models for some of your more advanced ideas ?
Kun's STEM models are much more complex and robust than my models. My
USA Ebola model was intended as a back of the envelope 'black swan'
simulation. However, I really appreciate the feedback you have given.
It will help make all the simulations more accurate.
I don't really follow how you describe the rate at which infected
individuals recover and die. If the infectious duration is given by
1/gamma and the case fatality rate is f, you can say that infected
individuals recover at rate (1-f)*gamma and die at a rate f*gamma. In
your model, the total rate at which infected individuals recover or
die is 4*gamma, that means that their infectious duration is also only
1/(4*gamma). Based on your parameters, that will be a duration of 4.1
days that actually is a good value for the infectious duration. But I
don't think this is really what you wanted to model, is it?
The problem was that I did not understand how STEM was doing the generic
SEIR death-rate calculations, so it was a learning process for me.
Some of my parameters were originally was a hack to work-around some
issues I did not understand in STEM. I noticed when my simulation ran
in real-time, STEM included the deceased in the R compartment. But when
I used STEM's 'post-simulation analysis' of the aggregated CSV log file,
STEM does NOT include deceased in the R compartment (the deceased were
recorded in their own spreadsheet column instead).
On top of the confusion from that issue, I noticed that when I was
adding a non-zero death rate 'Delta' AND keeping Beta (Transmission
Rate) constant, my R0 dropped below 1. It took me a full day of work to
realize the introduction of the death rate was responsible for dropping
the simulation's R0 below 1, and the only way I found to raise R0 back
up to the desired value was to scale Beta to account for the death rate
Delta.
See my notes on this here (which in hindsight may have been an error):
http://www.operonlabs.com/?q=node/4
Looking back using your information, I think the underlying problem was
that perhaps I was not calculating Delta (and possibly Gamma) correctly.
At the time, I devised a re-scaling of Beta based on the mortality rate
to keep R0 my desired value (1.83). . . The only problem was I had no
way to calculate Delta for STEM from an equation. . . By trial and error
testing, I determined an appropriate Delta from Gamma, which yielded
simulations with CFR of 71%.. . I think the problem was because I
re-scaled Beta to account for the mortality rate parameter and achieve
desired R0... Anyway, this was my quick work-around for getting Ebola
fatalities to work in STEM's Generic SEIR disease model. My mistake, it
appears, was to re-scale Beta and/or an incorrect calculation of Gamma
and Delta.
From what you are saying, I will have to investigate and re-run
everything. . . Based on your information, I should instead try this:
1. Leave Beta alone (perhaps don't do any re-scaling)
2. Set f = 0.71
3. Set Gamma_STEM = (1-f)*Gamma = .29*Gamma
4. Set Delta_STEM = f*Gamma = .71*Gamma
where Delta_STEM is the STEM fatality rate probability per simulation
cycle.
If this works, I will be ecstatic. Thank you for your suggestions on
how to fix these parameters. I will update and re-upload the STEM
models (both USA and West Africa) as soon as I figure it out.
1/(4*gamma). Based on your parameters, that will be a duration of 4.1
days that actually is a good value for the infectious duration. But I
don't think this is really what you wanted to model, is it?
You are correct -- this was not the intent at all! :) . . . but rather
the result of trial and error regarding mortality rate Delta_STEM.
Thanks for clarifying this . . . At the time I was learning STEM and
creating the Ebola simulation B2 , I did realize the reciprocal of
Delta-STEM was going to be 4.1 days, which I thought might be 'off'...
But I still kept getting 29% for the population that did not get
'killed' by the Delta-STEM parameter , meaning they survived the disease
at a rate of 29%, which was correct. Also I had 71% of the population
in my models that did die from the disease, which was also correct ...
I suspected I had an incorrect value for Delta_STEM based on it's
reciprocal, which as you noted was 4.1 days.
I'm going to re-run the simulations with your recommended calculations
for these parameters.
If your recommendations solve my Delta issues, I will go ahead and
re-upload the USA1 simulation along with a West Africa simulation I have
built as well (with both containing updated parameters based on your
advice).
Thank you for your time Dr. Althaus -- I really appreciate the feedback.
It has been very helpful.
It's really fantastic to get the feedback from epidemiology experts such
as yourself, the staff at IBM, and others to review my parameters, STEM
models, and STEM code.
Have a great weekend.
Sincerely,
Alex
On 2014-10-17 03:20, Christian Althaus wrote:
Dear all,
It is nice to see progress in the STEM modeling community. Thanks for
sharing. It is a bit difficult for me to attend the weekly telephone
conferences, so I thought I share a few comments through this mailing
list.
In my opinion, it is not very sensible to simulate a hypothetical
outbreak of Ebola in the US, assuming that all parameters are the same
as in West Africa. The R0 of Ebola in the US and other western
countries would clearly be lower, most likely below 1. That means,
that any import of cases could only cause a small outbreak as seen in
Nigeria for example.
The doubling time of a simulated epidemic is determined by your
assumed values of R0 and the average generation time. So it's no
surprise that the doubling time you observe is similar to the one in
West Africa. You could easily calculate the doubling time from your
formulas.
I don't think that the infectivity period is the same as the interval
from symptom onset to hospital discharge. People who are discharged
will not have been infectious for at least a few days. From the WHO
paper, I think it is better to look at the interval from symptom onset
to hospitalization (5 days) or death (7.5 days). Alternatively, you
can calculate the infectious duration as the difference between the
serial interval (generation time) and the incubation period, i.e.,
15.3 days - 11.4 days = 3.9 days. Remember that in your model you want
to know the time during which people do transmit, and not the time
during which they could transmit. If people are hospitalized quickly
and there is not much transmission in the hospital, that means that
the infectious duration can become shorter.
I don't really follow how you describe the rate at which infected
individuals recover and die. If the infectious duration is given by
1/gamma and the case fatality rate is f, you can say that infected
individuals recover at rate (1-f)*gamma and die at a rate f*gamma. In
your model, the total rate at which infected individuals recover or
die is 4*gamma, that means that their infectious duration is also only
1/(4*gamma). Based on your parameters, that will be a duration of 4.1
days that actually is a good value for the infectious duration. But I
don't think this is really what you wanted to model, is it?
Best,
Christian
_________________________________________
University of Bern
Institute of Social and Preventive Medicine (ISPM)
Dr. Christian L. Althaus
SNF Ambizione Research Fellow
Finkenhubelweg 11
3012 Bern
Switzerland
Tel +41 31 631 56 40
Fax +41 31 631 35 20
calthaus@xxxxxxxxxxxxx
www.ispm.ch [3]
www.immuno-epidemiology.ch [4]
On Fri, Oct 17, 2014 at 2:22 AM, <alex@xxxxxxxxxxxxxx> wrote:
I updated the STEM Wiki documentation and uploaded the Operon "B2"
Ebola model project for the United States. I will upload the West
Africa project as well shortly. My model predicts a 'time to peak
infected' of 375 days post-introduction into the U.S.
http://wiki.eclipse.org/Ebola_Models [1]
My results agree VERY CLOSELY with the observed multi-country
outbreak doubling time. (14.79 days in model, vs 15.74 days in
reality).
The latest Operon Labs 'B2' Ebola Outbreak Model SEIR parameters
are as follows (derived from the NEJM/WHO data):
1/σ (Incubation Period) : 11.4 days (Multi-day Exposures, All
Countries, Observed)
1/γ (Infectivity Period): 16.4 days (Interval from Symptom onset
to Hospital Discharge, All Countries)
σ (Incubation Rate/Day) : 1 / 11.4 days = 0.08771930
γ (Infectivity Rate/Day) : 1 / 16.4 days = 0.06097561
δ (Fatality Rate/Day) : 3 * γ = 0.1829268 (Try for ~71% Case
Fatality Rate)
R0 (Reproduction Num#) : 1.84 ( Weighted Avg, All Countries)
βstem(Transmission Rate) = R0 * (γ + δ)
βstem(Transmission Rate) = 1.84 * (γ + δ)
βstem(Transmission Rate): = 0.4487805
Experimental testing of the above parameters in the United States
with standard SEIR+D resulted in the following results:
Td_model (Model Doubling Time) = 14.79 days
Td_actual (Actual Doubling Time) = 15.74 days (Weighted Average,
Liberia+SL+Guinea)
Serial Interval (Model Serial Interval) = 19.6 days
Serial Interval (Actual Serial Interval) = 17.6 days
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[1] http://wiki.eclipse.org/Ebola_Models
[2] https://dev.eclipse.org/mailman/listinfo/stem-dev
[3] http://www.ispm.ch
[4] http://www.immuno-epidemiology.ch
