'flu for theorists

summary of the issues and stakes in the current 'flu outbreak from a more theoretical physics perspective...

Three years ago I did a Back of the Envelope Assessment for Bird 'flu:

"...So, why worry?
As always, because of the low probability, high risk scenario.
Taken at face value, there is a ~ 1/100 risk of a pandemic killing ~ 1 billion people worldwide and tens of millions in the US; this is no higher than the "mean risk" of a pandemic of ~ 1/1000 per year, even though I take the prior that we know of a probable impending pandemic with H5N1. So I'd call it a conservative estimate, with the true risk maybe twice as large!
Of course it is the virus we don't know that will probably get us..."

3D structure of the influenza virus from electron tomography (from NIAMS 2006 press release)

The dynamics of 'flu are quite simple - as a first approximation it is a damped exponential growth, with three possible growth curves:
sub-critical, fizzling after a few generations;
time averaged steady state;
and super-critical exponential growth.

Of course all the super-critical growth curves eventually saturate to a logistic growth curve and fizzle or become steady state.

Looking at the US: we've gone from 6 cases over a couple of weeks, to 20 cases at the end of last week, to 40 cases this morning.
Clear exponential growth, with doubling time of about 2 days; so everyone in the US will have come down with the 'flu by the end of May...

Well, maybe not.

Right now we are dominated by observer bias, having become aware of the existence of the new 'flu there is much more intensive monitoring, which will create apparent exponential growth even if the case numbers are fizzling. It will take 4-6 days to know if the true cases are really growing exponentially, once surveillance is at some near constant intensity (so cut Mexico some slack, figuring out how many cases they really have really is a hard problem taking many days to converge on, and the numbers may be changing for real).

So, then what? If the 'flu is fizzling, cool.
It may of course become endemic as a variant seasonal flu, or it may flare up again, like next year, as a more intense pandemic (this is a concern because it is new, it is the end of northern hemisphere 'flu season, and because that is what the 1918 pandemic did).

If it goes pandemic now, then what happens depends on the virulence and the case fatality ratio: basically how many people get really sick and how many of those die.
We do not know that yet, it is possible that a lot of people have already had this 'flu but the symptoms were mild and people didn't see a doctor or it was diagnosed as seasonal 'flu like illness.
This is one possible explanation for the difference so far in US and Mexico statistics (40 cases, one hospitalization and no deaths; vs 1600+ cases with ~ 150 or so suspected deaths).
On the face of it, the Mexican 'flu has case fatality ratio of 5-10%, which is very high for a transmissible virus and catastrophic in its implications. The US cases seem milder.
Or it could be Poisson noise in the US cases.

But, it is not implausible that there are actually 10 times or more than those reported mild cases in Mexico . Which would make the CFR reassuringly below 1%
(note that normal fatality ratio in the US for influenza severe enough to require hospitalization is in the 5-10% range, mostly for older people and infants - a bad 'flu season in the US might involve 300,000 hospitalizations and 30,000 deaths, but maybe 30,000,000 cases of mild 'flu requiring no medical care).

Global Security.org has a good web page on pandemic numbers

Crudely speaking:

• there is endemic 'flu, which in the US kills about 1/10,000 per year.
• about once per decade there is a more intense 'flu which kills ~ 1/1,000 per year
• about once per century there is a major pandemic which kills about 1/100 of the population (from ~30% getting sick and ~3% dying)
• yes, about once per millennium (NB small number statistics) there is a major pandemic which kills about 1/10 - at least for the last millennium, in the US

Yes, it looks like a nice power law, within the poor statistics, and the time averaged odds of dying are equal for different paths (but other things are still over all more likely to kill any given person at any given time)

So, right now we are waiting to see:

1) are the real case numbers growing exponentially

2) how many of the cases are severe, requiring hospitalization and intervention

3) what fraction of the severe cases die?

If this is the next big one, as bad as the 1918 'flu, then about 100 million people in the US might get it, assuming a vaccine can not be developed, manufactured and distributed fast enough, and maybe 3 million people would die.
World wide this would scale to 200 ~100 million excess deaths on a time scale of a year or so, which is horrendous, but not demographically transformative like a once-per-millennium Black Death scale pandemic. 100 million excess deaths is roughly doubling the mean death rate. Worldwide. For a year.

There is also evidence that this flu is demographically selective, it may be hitting healthy young/middle aged people badly, which is a tentative signature of bad pandemics, although it could be due to selective observer bias.
There are also likely to be individual and population variation in susceptibility, geographic co-factors, possibility of other opportunistic infections and general population health issues that factor in.
Also, initially more people who are seriously ill are saved through intervention, but, later the fatality ratio for severely ill people may get higher, because the medical personnel tend to get hard hit, and resources run out - not enough ICUs, ventilators, anti-virals etc.
In extreme pandemics people who would survive with minimal care (fluids and over the counter medicines to control fever) die because everyone else is too sick, or too scared, to care for them.

Oh, and the virus can change.

Finally, when doctors say a 'flu is `mild', they mean: you will be sick as a dog, and wish that you were dead, and it will take you weeks to get back to normal.
To them, mostly, "serious illness" means "you will die or be crippled if we don't actively intervene".
What you think of as "mild illness" an MD doesn't really think about at all.

It will be an interesting week or two as we watch the numbers come in.

There are much better and more detailed explanations over at Effect Measure

CDC swine flu page