The spread of disease is a well-studied problem. This work has provided numerous insights into the nature of harmful epidemics and the strategies for controlling or preventing them.

Harmful epidemics include flu and dengue fever in humans or bacterial wilt in beans. But epidemics don’t always cause harm and some can be beneficial. Examples include viruses that protect their hosts, and social phenomenon such as new feeding techniques among birds and the adoption of the new agricultural technology in humans and so on. Nevertheless, little is known about the way beneficial epidemics spread.

Today that changes thanks to a group of researchers at the Santa Fe Institute in New Mexico who have studied the nature of beneficial epidemics in detail for the first time. Their work could have significant implications for individuals and organizations who hope to exploit beneficial epidemics and, of course, for those who might want to prevent them.

The Santa Fe group began by defining the unit of transmission in beneficial epidemics as the “bene” (pronounced BEN-ay). A bene can be a virus, a gene, a technology, a behavior, an idea and so on—anything that confers an advantage and can spread through a population.

“At the most basic level benes have two hallmark traits: 1. they are transmitted horizontally and 2. they offer some benefit to their host,” says the Santa Fe group.

Clearly, some benefits can be transmitted from one generation to the next, such as genes. This kind of vertical transmission takes place over time scales measured over many generations.

However, the Santa Fe group is interested only in benefits that transmit horizontally. These include ideas, behaviors, viruses, and so on. These things all spread on time scales that are shorter than a single generation.

In particular, the group investigates the epidemic dynamics that result from benes that confer social benefits.

These benefits can have various consequences. For example, an individual excited about a new bene might begin trying to share it and a beneficial virus might increase an individual’s energy or happiness levels. This would increase the number of social contacts and the energy devoted to these contacts.

Crucially, in both cases the bene increases the number of contacts the individual has within the community. This has significant implications for the way beneficial epidemics emerge.

To explore these implications, the group created a computer model of the way a bene spreads through a hypothetical population of 1,000 people who have either been infected or are susceptible to infection. This model specifically examines the impact of connectivity on the way benes spread.

The results make for interesting reading. The group says the model reveals that beneficial epidemics spread in three different ways depending on the social structure and the various advantages and disadvantages for the individuals involved.

The first pattern of spreading they call “evangelical,” and it occurs when individuals attempt to spread the bene as widely as possible throughout the population. This is analogous to the spread of religions, which can sometimes spread explosively around the world.

A key feature of certain religious work is the conversion of susceptible individuals by infected ones—missionary work. When this happens, missionaries actively seek out individuals to convert. This is known as disassortative behavior, since individuals are seeking out others who are unlike them.

This behavior turns out to have an important impact. The ordinary spread of epidemics is well known to follow an exponential path which leads to explosive growth.

But in evangelical spreading the growth is even faster. And it continues until the entire population is infected. That’s because as the number of susceptibles becomes smaller, the number of individuals trying to infect them gets higher. The result is super-exponential growth.

But not all benes spread in this way. The Santa Fe group also identifies a pattern they call “cool kids” spreading, in which everyone attempts to connect to as many infected individuals as possible and as few noninfected individuals as possible. This is assortative behavior in which infected individuals seek out others like themselves. However, susceptible individuals also seek out infected individuals who try to avoid them.

The outcome is quite different in this case. “The result is a network composed of two blocks: one includes the susceptible as disconnected singletons, while the other includes the infected individuals which are interconnected,” says the Santa Fe group. In other words, this kind of behavior leads to cliques that end up excluding some individuals.

The final type of epidemic spreads even less effectively. In this case, infected individuals again seek out others who are infected. However, the susceptibles behave differently, seeking out either infected individuals or other susceptibles. “This also produces an incomplete epidemic spreading process that cannot proceed further,” they say.

The group calls this the snobs scenario. “The result of these rewiring strategies is that the network divides into two completely disconnected communities, and this prevents the epidemic from reaching the whole population,” they say.

All this has profound implications for the way benes spread through society. Some should spread superexponentially, infecting everyone in the blink of an eye. Others are destined only to spread through small groups or cliques who act in a way to prevent further infection.

But while the models provide interesting support for this idea, an important question is whether this actually happens in the real world. To find out, the Santa Fe group studied the spread of new words over time.

Neologisms can be thought of as benes because they create several advantages for individuals who use them. Speakers use neologisms to communicate new concepts or old concepts in a new way. But they also use them to assert their identity—in this sense, new words are fashion statements.

“For instance, the use of the phrase ‘personal computer’ could reflect that the speaker keeps up with changing technology, and may also be an intentional signal by the speaker to show an awareness of technological change,” says the Santa Fe team.

It’s possible to study the emergence of new words thanks to Google’s Ngram corpus. This records the number of times words have been used in books each year from 1500 to 2008. So it’s straightforward to see that the phrase “personal computer,” for example, emerged in the late 1970s, peaked in use in the late 1980s and has declined in popularity since then.

The team studied the word use trajectory of 48 beneficial words and phrases such as aspirin, microbrewery, chairperson, genomics, one night stand, and so on. And they found examples of all three types of spreading. For example, the word “chairperson” follows the evangelical trajectory spreading throughout society while “genomics” has followed the cool kids trajectory and is confined to certain cliques.

That shows how words that are widely useful and popular spread more widely and rapidly than words with limited use. “This pattern may provide clues to the process by which the beneficial epidemic of new word spread occurs,” they suggest. Clearly, words that have the potential to be more popular, that are naturally “sticky,” do better.

The pattern also suggests an answer to one puzzling question: why do harmful epidemics, such as diseases, seem much more common than beneficial ones?

The answer, according to the Santa Fe team, is that superexponential spreading means that benes spread much more quickly, so there is only a fleeting instant in which to observe their spread. And once a bene is established, it becomes difficult to distinguish from other memes.

Of course, a big part of this is the inherent “stickiness” of new benes when they first appear. That’s a topic of prime importance to governments, businesses, and marketers. If they can identify benes that spread superexponentially, they’ll have a powerful tool at their disposal. They may also be able to identify benes likely to occur in cliques (NIMBYism may be an example of this).

No doubt, these groups will be pawing over this work with interest.

An interesting corollary to all this is the way this research was produced. This paper is the result of an extraordinary scientific process called “72 hours of science.” Fifteen researchers at the Santa Fe Institute resolved to create a scientific paper in 72 hours.

In choosing the topic, the only criteria was that most members of the group must never have heard of the problem. The entire group share authorship equally.

The result was this study on beneficial epidemics. How quickly will it spread?

Ref: arxiv.org/abs/1604.02096 : Dynamics of Beneficial Epidemics