The S-curve and the epidemic

It’s been observed that over time networks grow along the shape of S-curves, where the flattening takes place when limits in network effects are reached. This is a phenomenon we’ve seen in the social networks, which often seek to boost the growth with new product introductions or, sometimes, by new network acquisition.

The desired outcome of such events isn’t only to increase the number of participants, or nodes, that are active in the system, but to increase the ways and reasons to engage, or ties between them. In combination, this should lead to greater network size and density, consisting oftentimes of more and bigger clusters. In commerce, this is a desirable result. In certain other cases, though, the better one would be its opposite.

Among the earliest research on networks and network behavior are studies about epidemics. In these cases, obviously, the objective is to stop, or at the very least slow down, the growth, arriving at the S-curve’s horizontal line more expeditiously, and hopefully at such a point before the numbers become large.

The quarantines and lockdowns are a way to cut the ties and isolate infected nodes and the surrounding clusters where the ties are strongest from the broader graph and weaker ties to nodes that haven’t been infected. The quarantines and lockdowns are not the only way, or not only quarantines and lockdowns literally.

The extra measures that are being taken – the travel bans, the work from home, the event cancellations – are precautionary steps to block network traffic and disrupt engagement where it’s most prone to happen. Another mechanism, a universal isolation in a sense, is the individual care being encouraged, such as the persistent cleanliness of hands, which is itself a way to reduce virus flow and disrupt links throughout the network.

I came across the video below on Brad Feld’s blog the other day, and strongly recommend it in its full 9-minute length. It illustrates, in simple terms, the math behind the epidemic network growth, and frames this post’s preamble in a quantifiable perspective.

Without spoiling any of the substance, the video concludes thus: “If people are sufficiently worried, then there’s a lot less to worry about.” I believe people are pretty worried, and this will ultimately reduce both the time and magnitude of the epidemic network growth. The architecture that brought Facebook and Twitter up, is the same to bring this other network down. Keep you hands clean, disengage.

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