Randomness a key in spread of disease, other 'evil'

January 2, 2018 by Tom Fleischman, Cornell University
Credit: CC0 Public Domain

An unfortunate church dinner more than 100 years ago did more than just spread typhoid fever to scores of Californians. It led theorists on a quest to understand why many diseases - including typhoid, measles, polio, malaria, even cancer - take so much longer to develop in some affected people than in others.

It's been known for more than 60 years that the periods of numerous diseases follow a certain pattern: relatively quick appearance of symptoms in most cases, but longer - sometimes much longer - periods for others. It's known as Sartwell's law, named for Philip E. Sartwell, the epidemiologist who identified it in the 1950s, but why it holds true has never been explained.

"For some reason, [biologists don't] see it as a mystery," said Steve Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics. "They just see it as a fact. But we see it as, 'Why? Why does this keep coming up?'"

Through mathematical modeling and application of two classic problems in probability theory - the "coupon collector" and the "random walk" - Strogatz and doctoral student Bertrand Ottino-Löffler propose an explanation.

Working with a in which chance plays a key role, they calculated how long it would take a bacterial infection or cancer cell to take over a network of healthy cells. The distribution of incubation times in most cases, they contend, is close to "lognormal" - meaning that the logarithms of the incubation periods, rather than the incubation periods themselves, are normally distributed.

This emerges from the random dynamics of the incubation process itself, as a pathogen or mutant competes with the cells of its host.

Their paper, "Evolutionary Dynamics of Incubation Periods," was published Dec. 21 in eLife. Contributing biomedical background was Jacob Scott, physician-scientist in the Department of Translational Hematology and Oncology Research at the Cleveland Clinic.

Reading Scott's blog, Cancer Connector, motivated Strogatz and Ottino-Löffler to study disease incubation dynamics.

"I saw a post about using evolution on networks to analyze cancer, which seemed interesting because cancer is very much an evolutionary disease," Strogatz said. "People including Jake have been looking at cancer from this evolutionary perspective."

The discovery that incubation periods tend to follow right-skewed distributions - with symptoms quickly developing for most people, with much longer periods for a few, so that the bell curve has a long "tail" to the right - originally came from 20th-century epidemiological investigations of incidents in which many people were exposed to a pathogen. For example, at the 1914 church dinner in Hanford, California, 93 individuals became infected with after eating contaminated spaghetti.

Using the known time of exposure and onset of symptoms for the 93 cases, California medical examiner Wilbur Sawyer found that the incubation periods ranged from three to 29 days, with a mode (most common time frame) of only six days. Most people were sickened within a week of exposure, but for some, it took four weeks to get sick.

As it turns out, nearly all diseases - and as Strogatz and Ottino-Löffler contend, most situations where "good" is overtaken by "evil" - follow this pattern of quick proliferation for the majority, with a few "victims" lasting longer before finally succumbing. The different levels of health and of exposure to the pathogen can certainly play a role, Strogatz said, but are not the determining factors.

Strogatz's proposal follows the "coupon collector" theory: Imagine someone collecting baseball cards or stamps in a series. If a random item arrives every day, and your luck is bad, you may have to wait a long time to collect those last few.

Strogatz admits that while it's tricky to generalize too broadly, this theory holds up following countless simulations and analytical calculations performed by Ottino-Löffler. And this could be helpful in explaining not only disease proliferation, but also other examples of "contagion" - including computer viruses and bank failures, the researchers say.

"In a very stripped down, simplified picture of reality, you'd expect to see this right-skewed mechanism in many situations," Strogatz said. "And it seems that you do - it's sort of a basic vocabulary of invasion. It's a powerful underlying current that's always there."

Explore further: Mathematician's study of 'swarmalators' could direct future science

More information: Bertrand Ottino-Loffler et al. Evolutionary dynamics of incubation periods, eLife (2017). DOI: 10.7554/eLife.30212

Related Stories

Professor quantifies how 'one thing leads to another'

August 15, 2014

(Phys.org) —"One thing led to another," people often say. Events, discoveries and relationships are triggered by something previous. The iPhone case was designed only because the iPhone was invented first. A song became ...

Three weeks since last Ebola case in Mali: WHO

December 17, 2014

Mali has not had a case of Ebola for three weeks, the World Health Organization said Wednesday, completing one of the two incubation periods the country needs to be declared free of the virus.

Explaining Why the Millennium Bridge Wobbled

November 2, 2005

Steve Strogatz has a penchant for things that happen in unison. So when the Cornell University professor of theoretical and applied mechanics (and author of the 2003 book "Sync: The Emerging Science of Spontaneous Order") ...

Entry screening won't stop SARS, flu

September 23, 2005

Screening air passengers as they arrive at British airports is unlikely to prevent importation of either SARS or influenza, researchers in London report.

Six degrees of separation: Why it is a small world after all

October 19, 2017

It's a small world after all - and now science has explained why. A study conducted by the University of Leicester and KU Leuven, Belgium, examined how small worlds emerge spontaneously in all kinds of networks, including ...

Recommended for you

Archaeologists discover Incan tomb in Peru

February 16, 2019

Peruvian archaeologists discovered an Incan tomb in the north of the country where an elite member of the pre-Columbian empire was buried, one of the investigators announced Friday.

Where is the universe hiding its missing mass?

February 15, 2019

Astronomers have spent decades looking for something that sounds like it would be hard to miss: about a third of the "normal" matter in the Universe. New results from NASA's Chandra X-ray Observatory may have helped them ...

What rising seas mean for local economies

February 15, 2019

Impacts from climate change are not always easy to see. But for many local businesses in coastal communities across the United States, the evidence is right outside their doors—or in their parking lots.

The friendly extortioner takes it all

February 15, 2019

Cooperating with other people makes many things easier. However, competition is also a characteristic aspect of our society. In their struggle for contracts and positions, people have to be more successful than their competitors ...


Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet Jan 02, 2018
"The different levels of health and of exposure to the pathogen can certainly play a role, Strogatz said, but are not the determining factors."

"but are not the determining factor" - pointing at some research or a brief explanation why this might be so would have been helpful right here ...
not rated yet Jan 03, 2018
"The different levels of health and of exposure to the pathogen can certainly play a role, Strogatz said, but are not the determining factors."

"but are not the determining factor" - pointing at some research or a brief explanation why this might be so would have been helpful right here ...

Random chance.
1 / 5 (1) Jan 03, 2018
Yeah, trying to pin down the ephemeral variations of constantly evolving biology?

Is kinda like trying to nail blobs of jello to the wall. No cooperation! And lots of frustration.

With a wildly swinging hammer in play? Someone is gonna get hurt. Possibly and most probably your own thumb!

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.