Swine flu: estimating pandemic potential with a computer model using early data

Trying to figure out where the incipient swine flu pandemic is heading and how fast it is heading there is shooting at a moving target, and this one is moving pretty fast. The best we can do at this point is use whatever information we have to make some educated guesses about different scenarios along with how likely various scenarios are. We used to do this on the back of an envelope, Now we use computer programs. I'm not sure we are doing much better (or much worse), but we can make use of more information and the answer looks prettier when displayed.

Expedited publication of such an assessment is now online at the journal Science. Imperial College (UL) modeler Neil Ferguson and an international team used available early data from Mexico and information on international spread to try to figure out how transmissible the swine flu virus is and take a measure of its virulence. Here's their summary:

Our estimates suggest that 23,000 (range 6,000-32,000) individuals had been infected in Mexico by late April, giving an estimated case fatality ratio (CFR) of 0.4% (range 0.3% to 1.5%) based on confirmed and suspect deaths reported to that time. In a community outbreak in the small community of La Gloria, Veracruz no deaths were attributed to infection, giving an upper 95% bound on CFR of 0.6%. Thus while substantial uncertainty remains, clinical severity appears less than that seen in 1918 but comparable with that seen in 1957. Clinical attack rates in children in La Gloria were twice that in adults (Science)

There have been a number of deaths from this virus (WHO tallies 53 as of this writing), mainly so far in Mexico, but without knowing how many people are infected (including mild and asymptomatic cases) it is difficult to know how virulent this virus is. This model tries to determine the rough size of that denominator. The estimates in this paper suggest the swine flu virus virulence to be comparable to the 1957 pandemic ("Asian flu," H2N2), somewhere around 0.4%. Seasonal flu has a case fatality ratio (CFR) of roughly 0.1%. As soon as you start to look at the assumptions that were made, however, you begin to see the level of uncertainty here.

The CFR has a numerator (number of deaths among the infected) and a denominator (the total number infected). The deaths may be undercounted in certain age groups (e.g., the elderly) where many competing causes of death may mask flu related deaths. On the other hand, not all deaths put down as flu related in the early phases of this outbreak, modeled in this paper, may be flu related. In addition, the data are what statisticians call "right censored," that is, the eventual outcome of many cases in the denominator was as yet unknown. At some point after they were counted as an infected case they may die from a flu related cause but wouldn't have been counted in the numerator. Special techniques, using time to event modeling, are often used to take deal with right censored data like these.

The denominator, the total number of infected, has even more uncertainty. Since many mild infections were probably missed in Mexico, the paper used the prevalence of infection among travelers as an estimate on the assumption there was more intense surveillance. Using this number the number of cases in Mexico was back calculated. But there are some assumptions, here, too:

Key underlying assumptions in this analysis are that the population mixing in Mexico is equally likely between Mexican residents and tourists, and tourists and Mexican residents are at equal risk of infection (despite demographic and other differences). If infections are concentrated away from traveler destinations, the number of people infected in Mexico will be under-estimated, and conversely will be over- estimated if the epidemic has disproportionately affected geographical zones visited by travelers. Under the assumption that reporting of infections in travelers was complete we obtained estimates of the number of infections occurred in Mexico by late April from a model of the interval-censored country case counts which varied between 18000 and 32000, depending on the mean duration of stay of tourists assumed, with perhaps the most credible single value (based on journey duration data) being 23000 [figure references omitted].

Other assumptions are possible, and Fraser et al. discuss some of them. The main point, however, that when viewing results of a paper like this it is best to consider them as highly tentative. As this unfolds further, we may get a better idea of virulence as expressed by the CFR. At the moment it looks similar to the 1957 pandemic virus, no where near as bad as 1918 but worse than seasonal flu. This wouldn't be surprising. But neither would a variety of alternatives, given the uncertainty.

Similar observations can be made about the measures of transmissibility and the timing of when the outbreak started. The authors consider the virus to be more transmissible than seasonal flu, again a characteristic of pandemic strains. But the uncertainties here are even greater than with the CFR and the assumptions are, too. Some of the more qualitative features are quite robust, however. It is pretty clear that we are seeing many generations of cases and that sustained person to person transmission is occurring.

Since we don't understand the dynamics of seasonality, we still don't know how the emergence of this virus in the "off season" affects things like severity and transmissibility (if at all). We're heading into flu season for the southern hemisphere, so we may learn more in the next few months.

The authors are frank about the uncertainties, as well they should be:

The future evolution of the transmissibility, antigenicity, virulence and antiviral resistance profile of this or any influenza virus is difficult to predict. It is also unclear whether it will displace existing influenza A subtypes from the human population, as occurred in the 3 last pandemics.

In other words, don't rely too much on the results of this first pass at the data. Unfortunately, despite all the caveats in the world, the fact that this was done "by a computer" is likely to give the numbers a life of their own. This isn't a slap at the value of modeling, something about which I am on record as favoring.

I just want to remind everyone not to make the models bear more weight than they are built to sustain.

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As far as I'm aware Imperial isn't part of UL anymore.

Death rate so far at 0.1% or less (since we know 2 of the cases had serious pre-existing conditions, they're part of the death rate but not representative of the effect on the general population). May it stay there.

Am I the only one getting a perverse pleasure out of watching this thing unfold in almost-real-time? It's the monitoring that's got me hypnotized.

Not being in public health, to me it still has an element of unreality about it, like watching Shoemaker-Levy slam into Jupiter--a big mess happening somewhere else.

By Lisa the GP (not verified) on 12 May 2009 #permalink

Oh, I was using only the US indications for 'death rate' there, in case y'all wondered what I'm talking about in light of the Mexican data-sans-denominator.

By Lisa the GP (not verified) on 12 May 2009 #permalink

Lisa, I too find this fascinating to watch. It's unfortunate we don't have the resources to test every case. The numbers would be very useful.

By Joe Six Pack (not verified) on 12 May 2009 #permalink

Dear Reveres,

Thank you for helping us all make sense of the headlines, anecdotes, and fragmentary data.

I have questions about flu seasonality and R0. If transmissibility (?) fluctuates seasonally, how can R0 be pegged for a virus? Wouldn't R0 be a moving value - a cyclical function of time (greater in winter and near 1.0 in summer)?

Do all influenza strains follow similar seasonal patterns? If so, can one use the April-May R0 for novel N1H1 and extrapolate from it how transmissible it will be during the ideal conditions of Dec-Jan-Feb?
Thank you for considering!

By Mark VanDerwater (not verified) on 12 May 2009 #permalink

Mark: You are correct. It is wrong to think of Ro as a feature of the virus. It is a product of the virus, the host and the environment. Different contact rates, patterns (network topology) and transmission probabilities will produce different Ro, etc. It is a useful measure but shouldn't be considered solely as related to the virus, but of the outbreak setting itself.

I agree with Revere that this study should be regarded as a first pass at the data and not a definitive statement of CFR or clinical attack rate. I do give them credit for explicitly stating their methods and the basis for their conclusions. This is in stark contrast to the CDC which keeps repeating "no worse than seasonal flu" without a shred of data.

The most important variable left out of the Fraser et al. study was Tamiflu administration, imo. Early cases in the US and Europe received it, as did their contacts. I hope the next study will look at outcomes with and without Tamiflu and provide projected CFRs for both situations. My prediction is that untreated new H1N1 will have a substantially higher CFR than treated H1N1. Given that there is insufficient Tamiflu, ICUs, vents etc. for more than a small fraction of the world's population, statements about "no worse than seasonal" flu are grossly inappropriate, imo.


New virus could still mutate, spark pandemic: WHO

Movement Restrictions + Stockpiles = Few or No Infections


I posted on here a couple of weeks ago my theory that genetics in Mexico played a significant part in the differences in outcome. Few seemed to agree with me. The above-referenced article is giving me a little "I told you so" feeling which I can scarcely contain. It's certainly worthy of further study, if nothing else!

By Lisa in Ontari… (not verified) on 12 May 2009 #permalink

Lisa: I would think this argues against your thesis. With so much diversity it is unlikely there is a single factor that makes the population more susceptible.

Basically these guys are saying the Mexicans and WHO are talking through their (10 gallon) hats... if, as they say, "23,000 (range 6,000-32,000) cases" and "14 to 73 generations of human-to-human transmission" the epidemic is WAY out of control and the WHO "confirmed cases" bares no relation to reality by an order of magnitude.

By John Carter (not verified) on 12 May 2009 #permalink

1) WHO is being criticized by some for not ramping up massive production of cheap Tamiflu for the Third World -- by overriding Roche's patent and ordering generic supplies from other companies. See http://www.chicagotribune.com/news/nationworld/sns-ap-eu-med-tamiflu-ge… and http://www.wired.com/wiredscience/2009/05/genericfludrug/

2) It seems to me that What was NOT mentioned in the News Stories was: a) Many victims do not currently require Tamiflu to survive the current virus and (b) widespread use of Tamiflu would make it more likely that a resistant strain of the virus would develop and that would screw High Risk patients who would currently be saved by Tamiflu.

But on the other hand, it seems that WHO should have a MUCH bigger stockpile of Tamiflu for rapid distribution in poor countries if this flu explodes -especially in the Southern Hemisphere. WHO wouldn't have to distribute it yet but should have it on hand. If Roche won't make it for a decent price, then WHO should go with generic production to build the stockpile.

Am I wrong?

By Don Williams (not verified) on 12 May 2009 #permalink

John: WHO's list of confirmed cases is just that, lab confirmed cases. They have never said or even implied that it is an accurate case count of all cases, a count no one can make. We can only estimate it indirectly, as this paper does.

Don: There are generic versions of Tamiflu in production and Roche will likely not contest it if a pandemic occurs. They've recouped their money many times over and they know they would be fighting a losing battle. As for resistance, it didn't depend on any selection pressure for the seasonal H1N1. The H274Y mutation that confers resistance probably was a hitchiker on some other phenotype that was more fit.

cool, the computer modelled range for actual cases in mexico matches almost exactly my in-brain-while-walking-somewhere calculation from last week.

Lisa, that genetics link you are feeling good about...What please was the cause of death and or infection? Humans, birds, pigs, monkeys? Do you know what in particular they died of? We have to have the vector first and there so far is only the first patient connection and two or three others... Epidemic that does not make.

Genetic predisposition would mean they have have ruled out age as a factor and thats not the case. In fact it might just mean that they had no resistance due to no prior exposure. Then you have to add in the fact that it quit killing apparently within about 2 weeks which would indicate that something fundamental happened. Did we run out of genetically predispositioned to death Mexicans?

Oh I am glad it stopped because that initial CFR would have scared the shit out of just about anyone. The attack rate was very strange too and there were lots of suspected cases in there that were over 55 years of age. So was it age predisposition or genetics..? How about the NYC school kids? They were of the right age but none of them died thankfully. I wouldnt jump up just yet until there is a clear and direct link to genetics. There might indeed be something to it but there is nothing yet to really suggest anything other than a novel and rapidly evolving virus took a bunch. But what was the killer factor in the bug?

We dont even know for sure what most of them died OF. It would seem they just sort of shuffled off due to a number of causes. Deadie posted on it here last week and it was a marvel of thought (attaboy Deadie) and one that I hope wasnt right. If this mother is or was able to do the things he suggested then its a superbug in its own right.

Briefings given as of late keep asking but getting no answer to the nagging question and that is simply, "What killed these people?"

Still waiting for the answer as the virus now is into China, Indonesia (tonight) and all sorts of H5N1 infested countries. I just hope it doesnt bind up else we might yell in the night and get nothing but a big echo a year from now.

By M. Randolph Kruger (not verified) on 12 May 2009 #permalink

I have been trying to communicate with RTs in Mexico, and there may be a/(an unoficial) gag order in place. Normal channels, (I am from S. Texas previously) are closed. What typically kills patients in normal/severe flu of the "upper airway" is aveolar filling respiratory failure w/ or w/o bacterial pneumonia and probable sepsis/complications of co-morbidities. This last flu (mild year), I cared for abour 10-12 such fatalities. So far, there is no indication that this virus causes the "cytokine storm" ARDS as seen with H5N1, whose dining habits are closer to lower airway cells, (alveolar tissue), thus causing the "storm".
My conceren is that this bug (H1N1) could learn this nasty habbit while visiting Asia.

By Richard Mitche… (not verified) on 13 May 2009 #permalink

A NY Times article (http://www.nytimes.com/2009/05/13/health/13fever.html?hp) says that flu expert Dr. Richard P. Wenzel found that about a third of the patients he examined in Mexico who had A/H1N1 did not develop a fever until the disease had progressed, while some never developed a fever.

Does this suggest that A/H1N1 is more benign than thought, more dangerous (because without a fever a carrier is less likely to seek medical help, and more likely to remain socially active)?

Also, does this suggest that a far greater number of folks who actually have A/H1N1 are not being tested and that the disease is more widespread than thought?

By River the writer (not verified) on 13 May 2009 #permalink

A NY Times article (http://www.nytimes.com/2009/05/13/health/13fever.html?hp) says that flu expert Dr. Richard P. Wenzel found that about a third of the patients he examined in Mexico who had A/H1N1 did not develop a fever until the disease had progressed, while some never developed a fever.

Does this suggest that A/H1N1 is more benign than thought? More dangerous? More contageous? Seems many A/H1N1 carriers without a fever are less likely to seek medical help and more likely to remain socially active.

Also, does this suggest that a far greater number of folks who actually have A/H1N1 are not being tested and that the disease is more widespread than thought?

By River the writer (not verified) on 13 May 2009 #permalink

River: About half of seasonal flu (which is not benign as an illness) is asymptomatic. We don't know the extent to which an asymptomatic infected person can infect others, since they shed much less virus. But everyone believes there is much more infection than is being tallied. That's not controversial.

Thanks, Revere. The article suggests that the absence of fever in flu cases was atypical, and the high percentage of those infected with A/H1N1 without a fever was both rare and worrisome. I appreciate the clarification!

Be well!

By River the writer (not verified) on 13 May 2009 #permalink

better one model than none
ignore those who do give no estimate
and concentrate on those who do

anon: What if the one model is completely wrong or misleading? Better than none?

once you know it's wrong and misleading this knowledge
performs already a second (improved) one
until then you can't know

Ferguson in interview now said, he doesn't predict 3-4M deaths as in 1957 since we have vax and antivirals now.

Zambon compares it with 1968 or 1957

Racaniello also estimates CFR=0.4%

Woodson sees a 30%chance for >200M deaths

revere - ./.

Palese: 50% chance it will die

add other estiates here

anon: And where's your estimate? Which is more informative. Someone who takes a guess or someone who says we don't know and any guess is more or less arbitrary? If I asked you to give me the Dow Jones index in one year, should I act on anything you say?

Revere -
Most of the Mexican fatalities were treated very late, after 5-7 days of fever and coughing. When they started publicizing the flu, people started coming in sooner, getting treated sooner, and deaths went way down. It's what you would expect of any disease where good supportive care and antibiotics/antivirals can make a difference.

By Tsu Dho Nimh (not verified) on 13 May 2009 #permalink

my estimate(expectation value) was 20M deaths,
posted to the forums, down to 15M now due to
lack of spread outside North America and some other
strange patterns. Panflu probability contract
is actively traded by me at idea futures, currently
~40% for a pandemic in 2009
My estimate of the DOW would be only one of very many
and I don't claim for expertise. 8000 by Dec.2009