This is an interesting concept to consider.  Should politicians repeal helmet laws, knowing full well that the vehicle operator is fully responsible for their own health and safety, or is the simple change of the law enough to provide incentive signals.  Maybe we’d see an increase in the number of people on the organ donation list and their families targeting unhelmetted bike riders on the street with their cars.

From The Renaissance Mathematicus, we have a very interesting post, A loser who was really a winner.  It’s a tale of Christoph Clavius, educational reformer who played a pivotal, if oft forgotten role, for the 17th century mathematics revival and astronomy.  As an extra treat blogger Thony Christie is presenting a more detailed lecture version this post at the Remeis Observatory in Bamberg at 7:00 pm on 24th June (for those of you in the area… I wish I could go).

From Nature networks I, Editor blog: Henry Gee searches for the origin of the term “the missing link.“  Ben Zimmer helps on the Visual Thesaurus.

Ethan Siegel from Starts with a Bang has a great (and lengthy and on-going) series on the last 100 years of physics and astronomy.  Start (but by no means stop) with this post.

Here’s a post that may not be safe for work.  the Evil Monkey Scicurious, from Neurotopia v2.0, blogs about Grafenberg’s 1950 paper on “the role of the urethra in the female orgasm” published in the (you can’t make this stuff up) International Journal of Sexology.  The post is chock full of great quotes that would make you blush if you read them to your grandmother.

Brian Switek of Laelaps writes about an interesting hypothesis, about Charles Darwin’s ideas of origin of human races and genocide pursued by Western powers against indigenous people of the “new world” during his time.  In another post, Switek discusses Richard Owen, a 19th century anatomis, attemps to classify the Thylacoleo.

I’m honestly not sure how this one classifies as classic science.  But, Greg Laden submitted the post himself, so maybe he can help enlighten us?
edit – Greg Laden explains the background behind the post in the first comment, below

gg from Skulls in the Stars enlightens us on Barkla’s demonstration that x-rays have polarity (1905).  As usual, gg does an incedible job, gives an extensive background on x-rays and goes into great detail on Barkla’s experiments.

Last, but not least, my own post.  I talk about a paper which provided one of the origins for mathematical epidemiology, W. O. Kermack and A. G. McKendrick 1927 paper on their model of epidemic infectious disease.

Don’t forget, to vote for your favorite entry!  The winning blog author (which will be decided by, lets say, next week if there is a clear winner) wins a $20 gift certificate.  You have to be a registered member of SFN to vote in the poll, but if you leave a comment or send me a private email I can get your vote counted – or just register at the forum. It’s easy, free and fun.

This has been done using dynamic differential equation models for a long time now (and they can get quite complex).  The most common of these models is called the SIR model (which stands for Susceptible -> Infected -> Recovered) representing the dynamic conditions of individuals within a general population as they “flow through” these different disease states at various rates.

The first ‘discovers’ of the simple SIR model was W. O. Kermack and A. G. McKendrick in 1927, in a paper published in the Proceedings of the Royal society of London. Their model is, ex post, appropriately titled The Kermack-McKendrick model.

The paper itself goes through some complex derivations but the results are suprisingly simple and intuitive. In a closed population, N, where there is no population growth, they assume instantaneous disease incubation, homogeneous population with no age, spatial, or social structure and fixed transmission and recovery rates.  The result is this:

The susceptible population, which is the total population at t=0, decreases as an infection spreads and individuals become infected.  This occurs at the constant rate of β as a function of the number of infected individuals (the source of new infections) times the number of susceptible individuals (where the infectious agents are spreading to).  This means that to sustain an epidemic a disease requires a healthy reservoir of susceptibles or risk “burning” itself out.  This equation looks like this:

The dynamics of the infected population depends on the growth of new infections minus the recovery rate (or even death rate) or infected individuals, in much the same way that was described for the change in susceptible population:

Finally, the infected population recovers at a constant rate, γ, at some fraction of the population.

They get a pretty simple model, which they solve mathematically, but, with all these assumptions, can they get any useful data?

Yes!

If you can’t read the chart’s description, this is an epidemic of the plauge on the “Island of Bombay” which fits the The Kermack-McKendrick model for epidemics quite precisely.  When the infection gets introduced, although there are plenty of susceptible individuals around, the infection grows slowly (because the number of infected individuals starts out small).  However, the exponential trend takes off as the disease creates many new infections (which in turns create more new infections) .  But then the disease level crashes as it runs out of new individuals, as individuals recover or, in this case, they die.  Whereupon the epidemic is over.

Can we describe or predict the time evolution of an epidemic in a more general way?

Yes (according to the Kermack-McKendrick model)!

The so-called time evolution of the model is described by the so-called epidemiological threshold:

Ro can be thought of as the ‘potential’ for new infections, or the number of secondary infections caused by a primary infection.  When Ro < 1, the number of secondary infections is falling, and so the infection is dying out.  When Ro > 1 each infected individual will infect more than 1 other person, thereby causing the infection to spread positively within a population.

This quantity Ro (the details of which differ depending on the specific model being used) has been described as one of the most important variables in epidemeology, with consideration for disease transmission potential and therefore disease evolution (in more complex considerations).

Despite the fact that the model’s assumptions may not accurately reflect most real human diseases, Kermack and McKendrick come up with genuinely interesting and relevant conclusions.   They find that a population level requires some threshhold value in order for an epidemic to occur, a population size under this threshhold (which is disease specific) will not experience and epidemic.  An infection in a population that exceeds this threshhold will reduce the populationas far below the threshhold as it was above it.  Small increases in the infectivity rate can lead to dramatic changes in the dynamics of an epidemic, making them stronger.  Epidemics generally end well before the entire population of susceptibles has been exhausted.  Similar results are seen for diseases transmitted through an intermediate host (like vector bourne diseases).

Although this differential equation model lacks the accuracy of more complex models which relax assumptions and new types of stochastic models, the field of epidemeology has a lot to thank Kermack and McKendrick, for basically creating a new branch, bridging biology, mathematics and medicine.

I have some good news for bloggers: our good friend A Bear’s Key has generously offered to contribute 5 bucks to the prize pot, bringing the total prize for the winning blog up to $20 (redeemable in gift certificate form).

So get those entries in and, if you want to win the prize, make them good!

The result is interesting:

Can anybody figure out why Journal of Biol Chem is so much higher than Cell?  This surprised me a bit.

H/T Dr. Jekyl and Mrs. Hyde

I am quite pleased to announce that, since The Secret of Newton blog seems to have gone off the grid, duties to host the classic science blog carnial, The Giant’s Shoulders, has fallen to yours truly!  A special thanks to gg at Skulls in the Stars for giving me the opportunity to host and organizing everything (for every month for almost a year now).

The rules for blogging are still the same… blog about a classic science paper/experiment in your favorite scientific discipline.  After you’ve done that send me the link by leaving a comment here or dropping me an email by June 15th.

I’m also happy to announce my own personal addition to carnival  #12.  Whoever has the best post (determined by some fair voting system TBD) will win a $15 Amazon gift card (or different website of the winners choice).

Yes, I know it’s not much, but hey I’m financing it myself – and I’m technically unemployed right now!

I suggest that maybe we should attach our letters to fruit to bring down the mailing costs!

Dunbar also asks why a kiwi, banana and apple cost about the same, even though the apple is coming from much closer (probably upstate New York) and banana’s are pretty robust to ship.  So Dunbar posits the question to Will Masters, an agricultural economist at Purdue.  The answer, of course, is about supply and demand but Masters’ reply is a must read even if you already think you know the economics…

Damn supply and damn demand:
Why cheap hogs and costly ham?
Bargain wheat, expensive flour,
The oldest villain’s market power.

Just one seller makes us nervous,
Like that U.S. Postal Service:
They may offer bargain prices,
But who disciplines their vices?

Middlemen have long been blamed
For every market that’s inflamed,
Yet better explanations come
From many a Hyde Park alum.

Modern views from Chicago-Booth
Give a nuanced view of truth,
Steven Levitt and John List
Made each of us a freakonomist.

We let data speak its mind
No matter what Friedman opined
And find the price of fruit and veg
To be driven by the market’s edge.

Like the tail that wags the dog,
Marginal thinking clears the fog:
Sellers, buyers, traders too,
Interact and prices ensue.

A kiwi costs 33 cents
Simply because no one prevents
Another farm or New York store
From entering and selling more.

In contrast apples may be dear,
For reasons that will soon be clear:
Picking them’s below our station,
To lower costs we need migration.

Bananas have a different story,
Seedless magic, breeder’s glory,
Cheap to harvest and to ship,
Who cares if workers get paid zip?

Each crop’s method of production,
Where it grows and how it’s trucked in,
Satisfies some needs quite cheaply
While other costs will rise more steeply.

A buyer’s choices matter too,
For nonsense stuff like posh shampoo,
Prices are not down to earth,
The more you pay the more it’s worth.

Behavior is as behavior does,
Maybe some things are “just because,”
Much of life’s a mystery,
A habit due to history.

For prices, though, it’s competition
Plus tariffs set by politicians,
That determines whether we see
Such delightfully cheap kiwi.

I wonder how the group is able to solve the collective action problem against social pressures of not looking foolish in public.

This map would would put the island somewhere between South America and Africa. Or somewhere completely different than that.

UPDATE: The alleged debris apparently does NOT come from the Air France flight.  The plan and passengers are still Lost.

H/T – Greg Mankiw