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Perhaps some of you are interested in a more quantitative statement about the spreading of the Swine Flu (H1N1) infections worldwide with time and the corresponding behaviour of fatalities (red curve).

I plotted the following first 19 days since the outbreak using the official numbers from the WHO.


[EDIT:] For an updated and much improved diagram see further below!



As a rule of thumb, during about 2 weeks, the number of infections almost doubled within 4 days. As long as this law would hold, we face an exponential growth which sounds frightening! An exponential growth would correspond to a straight line growth in this semi-logarithmic plot. As you can see, the growth is less than linear overall (fortunately for now).

Some background math:
----------------------------------
Suppose, we have a law:
n = const. * a^t
and a doubling of the infection rate n2/n1 = 2 in t2 - t1 = 4 days
n2/n1 = a^(t2 - t1) = a^4 = 2
This determines a
a = 2^(1/4)

Therefore, a doubling every 4 days indeed corresponds to an exponential growth!

+++++++++++++++++++++++++++++++++++++
n = const. * 2 ^(t/4) = const. exp (ln(2)/4 *t) ; with t expressed in days.
+++++++++++++++++++++++++++++++++++++


More recently, however, the growth might show a tendency of flattening out...

Fridger

Is comparable data available for other types of flu?

selden wrote:Is comparable data available for other types of flu?

In case of the seasonal flu, global data are more difficult to administrate, since the seasons and the corresponding outbreaks of the flu are time shifted relative to each other.

About the seasonal flu in Germany, I do have national data from the Robert Koch Institut, our leading authority in these matters. The info is written in German, but there are lots of diagrams that are easy to interpret.

http://influenza.rki.de/index.html?l=de


Fridger

My numbers about the Swine Flu also demonstrate impressively that meanwhile the USA are the nation with far leading number of H1N1 infections world wide. That number exceeds the one in Mexico meanwhile by more than a factor of TWO. As of today, there should be above 4500 H1N1 infections in the US with the global number being ~ 8000. Germany is still far down at only 14 (no fatalities yet).

At my lab (DESY) we are having three very big international conferences this summer with hundreds of American physicists participating in high density packaging

By that time an extrapolation of the previous functional behaviour would predict far above one million infected people in the US (actually 4-5 million!) ...So let's hope for some saturation miracle. Many people have never contemplated the devastating growth of exponential functions.

Fridger

This should be put into perspective. Annual world deaths from the seasonal flu is estimated from 250,000 to 500,000 each year. I think about 20,000 to 30,000 are in the US. Statistics vary depending on the source.

The swine flu so far has killed less than 200 people that we know of. What you are seeing here is a media driven panic just like what happened with S.A.R.S. a few years ago.

Reiko wrote:This should be put into perspective. Annual world deaths from the seasonal flu is estimated from 250,000 to 500,000 each year. I think about 20,000 to 30,000 are in the US. Statistics vary depending on the source.

The swine flu so far has killed less than 200 people that we know of. What you are seeing here is a media driven panic just like what happened with S.A.R.S. a few years ago.

Reiko,

panic is entirely inappropriate, but rather the task is to monitor the virus precisely, because of its potential danger. Right now very few people are actually under a substantial risk. But the genetic structure of the virus (i.e. a mix of bird, swine and human flu pieces!) is such that it might well become an agressive killer after another (slight) mutation. This was also the case in the devastating flu of 1918 where the virus started off also relatively harmlessly, but in the second and third wave of outbreak (during the seasonal flu time) , it killed up to 50 million people worldwide! We were simply lucky with S.A.R.S, since despite it's danger the virus remained relatively little contageous for humans...

What I wanted to illustrate and document above was that people should start developing a feeling for exponential growth laws characterized by a doubling of the number of infected people within a constant time interval (say 4 days). Such laws always appear seemingly harmless initially, but then tend to "explode" due to the exponential behaviour.

time cases
-----------------------------------------------------------------
19 days.............................4 500 (e.g. like in the US as of yesterday)
1 month...........................36 000
2 months....................6 510 000
3 months.............1 402 840 000

These numbers correspond to an extrapolation of the present trend, that the number of incidences could well continue to double within a time interval of 4 days. If you count a death rate of only 1%, you come up to pretty big numbers of fatalities.

Aids also follows such a law! The main difference being that people didn't die as fast after their infection and lots of people didn't make their problem public for a while...

I should add that in my diagram at the beginning of this thread, the first data point was actually a lower limit. Hence the actual number of infections could have been substantially higher (Mexico!) in these early days, whence the exponential law would look correct all the way from the beginning...

Fridger

Below, I have updated my H1N1 data collection from above. Note the curves only contain official WHO numbers of registered, proven H1N1 infections (blue) and fatalities (red)! The last dots correspond to todays WHO numbers. The first entry corresponds to April 30th.

After adding a lot more official WHO points, it seems now quite suggestive that the growth is weaker than exponential, if the total behaviour is taken as a judgement.

Fridger

The problem with the mass-media in our modern sound-byte cultures is that they are not very good at communicating the real facts and issues, and tend to focus on the sensational.
Whilst in this case there was (as always) an element of media hype, this was not completely without good reason. I believe that it was the WHO who raised the alarm about this, and they usually don't do so without good reason.
There are a number of factors that affect the "pandemic risk" of a particular virus, including: how infectious is it, how long is the infectious period before onset of symptoms, death-rate. transmission method(s) (ie. is it airborne?),...etc..

As I understand it, the main concern which the WHO have had with H1N1 is that it is new in humans, so there is no natural immunity in the population, and no specific drug treatments, or vaccines available to treat it, and it's quite infectious (via airborne transmission)
On the plus side, because symptoms appear quite early on in the first few days of infection, and the infection either kills the victim or burns out in a couple of weeks, so far it's been relatively easy to identify victims early on, and quarantine them.

"Fast-burning" viruses will usually burn out before they can spread too far, whereas a slow burning virus can spread around the world before it's even diagnosed. (eg HIV/AIDS which remained hidden and undiagnosed for decades while slowly spreading around the world, purely because it takes years to kill it's victim)
NOTE: even though HIV is not a very infectious disease, I believe that it IS considered a pandemic by WHO's definitions because of the difficulty in preventing it's spread because of it's long gestation period.

A major pandemic risk that exists today which didn't exist in 1918 is the prevalence of international air travel -- note that the 1918 flu virus still managed to spread around the world even without this modern transmission vector.

Imagine if the H1N1 virus had been infectious for several weeks or months before symptoms appeared...(We probably wouldn't be sitting here discussing it now!! )

Mandatory reading IMO for anyone interested in viruses is:
"The Hot Zone" by Richard Preston - "A terrifying true story"
World famous horror writer Stephen King said this about it: "One of the most horrifying things I've ever read"

I've been through this before guys. It sounds scary because it's a variation you don't see often but it has been here before. The thing about the flu is it's always changing. You see a new one each year and get your vaccines only because it has popped up in the east first.
So now you have a different strain pop up right in the middle of flu season that scares everybody silly. It might change into something deadly, it might become more resilient. That's how it is with all flu strains. They all have the potential of mutating into something more virulent. The 1918 pandemic 91 years ago? Keep in mind the state of medical knowledge back then along with sanitary conditions. You had large populations in primitive conditions.

Keep track of this? yes of course but be scared of it? no.

Perhaps an update of the swine flu trend as of today (May 24 2009) with the latest official WHO numbers is of some interest. My previous diagram was from 4 days ago. Already then it seemed to become increasingly apparent that the growth law is weaker than exponential. An exponential growth would mean a straight line behaviour of the data in a semi-logarithmic plot. A convex shape as we presently observe, would indicate a weaker growth.

Here is the latest semi-log plot:



Actually, if you ignore the first week, the growth seems now pretty well linear, as this linear scale plot of the same data illustrates:



Fridger

Unfortunately, there is the following news that is a bit frightening:

USA geben auf

23.05.2009 - Keiji Fukuda von der WHO best?tigte gestern, dass die Zahlen der WHO nicht mehr die Wirklichkeit repr?sentieren. Die Labore k?men teilweise nicht mehr hinterher, die ganzen neuen Verdachtsf?lle zu pr?fen. Aus diesem Grund h?tte die USA aufgegeben, die F?lle der Infektionen zu z?hlen. Gepr?ft werde nur noch ein schwerer Krankheitsverlauf. Damit ist besiegelt, das eine enorm hohe Dunkelziffer entstehen wird und der ?berblick verlohren geht, wo sich der Virus aktuell aufh?lt. Ein be?ngstigender Gedanke. (Quelle: ?rzte Zeitung)

USA are giving up:

May 23, 2009: Keiji Fukuda of the WHO confirmed yesterday that the WHO numbers do NOT represent reality anymore. The laboratories are now partially unable to follow up with the high work demand of checking all the submitted cases. For that reason the US is said to have given up counting the number of infections. Only severe cases are kept track of. Therefore it is now definite that a BIG dark figure has started to develop. A frightening thought that the overview is getting lost as to the whereabouts of the virus...


The apparent flattening of the growth trend from my previous mail may be nothing but a reflection of that described fact!

Fridger

Swine who?

Serious stuff? Yes! Overblown with media sensationalism? YES!

(careful, strong language in image link below)
http://images.huffingtonpost.com/gen/77627/original.jpg

LordFerret wrote:Swine who?

Serious stuff? Yes! Overblown with media sensationalism? YES!

(careful, strong language in image link below)
http://images.huffingtonpost.com/gen/77627/original.jpg

Actually, over here, there is very little media coverage meanwhile, because many people show your kind of reaction ... My numbers are taken from WHO reports for medical doctors.


Fridger

Hi all,

while apparently many of you just prefer to ignore what is going on at the Swine flu frontier, let me nevertheless provide a little "scientific" update for those few who care...

From the WHO numbers there is evidence (although not compelling) that the world-wide growth law for H1N1 infections has changed from a rather harmless linear one with time to a much more dangerous (weak) exponential law, as I discussed previously!

This evidence arises even in view of a considerable dark figure from the United States. The US being meanwhile a world leader (what else did you expect ) as to the number of H1N1 infections (> 11000), have given up communicating all H1N1 infections some time ago. Only the severe cases are being reported since some time.

Here are the latest plots based on confirmed WHO data.

First, I show a semi-logarithmic plot, where a straight-line growth would signal a dangerous exponential increase of infections with time!



As you can see from the black straight line that I added to guide the eye,

n_exp = 8128 * exp( (t-16)/21.5),

a weak exponential growth NOW fits pretty well during the last 20 days or so!

The black straight line is normalized to 8128 infections at day 16 after the start of recording. Notably, it corresponds to a doubling of the rate in 14.9 days and

an increase by a factor of 1000 every 148.5 days. Hence after less than 300 days, the number of infections would be 1 million times what we have now....


For comparison, I show next the same data in a linear plot, again with a best fit straight line (black) for linear growth. You can see that recently, there seems to be a tendency for a stronger than linear growth...



Finally, it might be interesting to look at the history of the individual infections in Germany:
In Germany the flu was mainly imported by travellers to the US and Mexico:

• 30 by people returning from the US
• 9 by people returning from Mexico
• 1 by people returning from the UK
• 9 infections were from within Germany, with 7 in families of people returning from trips to the above countries. One infection happened in a hospital (a nurse) and one on a German Airport.

So the chances are still pretty low for Germans to catch the virus accidentally from some other German...

Fridger

EDIT, June 11th, 2009: The WHO has corrected it's latest data both for June 10th and 11th towards significantly higher numbers. I have replaced my plots below to account for this. They are now referring to June 11th.


Hi all,

today, the WHO announced the highest warning level 6 for the Swine flu. With this highest level 6, we now face officially a Pandemic! The reason is that meanwhile the virus has spread to 79 countries worldwide, and there is an increasing number of infections in countries different from the country where the Swine flu originated (Mexico).

Since about 1 month the growth law of the number of infections follows closely an exponential behaviour, with a doubling of infections every 14.9 days.

n_exp = 8128 * exp( (t-16)/21.5).

So roughly every two months the number of infections increases by a factor of 16. Of course, one assumes that by now there exists a LARGE dark figure of cases that were never reported. The WHO estimates that it is around ~ 100000 infections, i.e. already much larger than the officially recorded number of ~29000 as of today!

Here is the latest semi-logplot of the recorded data (as of June 11th) for worldwide infections (blue) and fatalities (red). The black straight line corresponds to the above exponential growth law! You see clearly that it fits pretty well since about one month...



You can also see from the linear scale plot of the same data that a linear growth law is definitely too weak by now!



Fridger

It may be comforting that the ratio of fatalities / H1N1 infections so far decreases linearly with time. Correspondingly, 1 month ago, at day 16 (May 15) still about 1% of the flu patients died while by today the death rate has decreased to about 0.5%, as you can see from this ratio plot of the official WHO data:



Probably, this is due to more people being now alerted about the necessity of seeing a doctor immediately after suspicious symptoms occur! Otherwise Tamiflu etc cannot be efficient.

Altogether, the death rate is fortunately (still) VERY low. Yet e.g. in the second flu wave during the coming fall/winter this may drastically change due to co-infections with the seasonal flu along with possible aggressive mutations of the virus...

Therefore it is stongly adviced by experts to take at least a vaccination against the seasonal flu this fall.

Fridger

Therefore it is stongly adviced by experts to take at least a vaccination against the seasonal flu this fall.

Got mine already.

During the past days, the characteristics of the Swine flu developped a tendency to aggravate, according to the WHO. Also today, the number of daily new infections has reached a record (5920 new infections worldwide over the weekend!).

Here are the actualized plots as of June 15th 2009:

Still an exponential growth law, even with a tendency of recent steepening...



The death rate continues to decrease (fortunately)


A linear growth is now ruled out by FAR, as this plot shows in comparison with the black straight line extrapolation from the early days...



Fridger

Find below the latest plots as of June 18th 2009.

Still exponential growth, with slope somewhat increasing, recently...


Death rate still decreasing linearly ...


Linear growth law dramatically excluded.


Yesterday, we even had the first Swine flu case in my small town out of Hamburg. A guy, 28 years old, who had returned from a 10 days stay in New York...

++++++++++++++++++++++++++
How about Swine flu infections among Celestians??
++++++++++++++++++++++++++
Statistically, it's about time, notably given our high American share...

Fridger

Today came again the weekly numbers from the US:

USA:
Total infections: .......... 21449
New during last week: .. 5657
Total fatalities: .....................87

Hence almost half of all recorded infections (47881) are now in the US...
During last week only, the number of fatalities in the US jumped from 44 to 87

Fridger