Viral growth and population size

I did it again. Oops.

Previously i made a statement about how infection spreads faster in a small community. It turns out that I was wrong. I ran the simulation for the estimate for the total number of internet users in the world and Estonia and, blimey, the numbers came out the same – in both cases, the growth rate is the same up to the point of explosion. When that happens, the larger population, naturally grows faster and flatlines on a higher absolute number (but, curiously, on the same relative percentage). This comes down to the fact that while a smaller population increases the probability of contacts with the infected person, it also decreases the contact frequency by the same fraction.

And yet, I can’t help but to feel the population size should matter. Our social networks are not uniform, there are clear clusters of people around. There is also clear empirical evidence with Facebook growing in small communities first and obscure countries like Estonia being over-represented in places like Orkut. But the model presented in the previous post is pretty damn irrefutable, anything I can think of is basically an extension of the same model and thus is likely to exhibit the same behavior. The reason, I believe is in the infectivity rate. I think that the network can go exponential locally. If the particular way a particular network implementes infectivity matches with the particular modus of social interaction within a community, the infectivity rate between the members of the community goes up and the network gains speed. And this, of course, is easier to do locally than globally. One might have a very particular idea about what exactly Estonian teenagers are thinking about right now (think but it is much harder to devise something that appeals to Estonian, British and US teenagers as well as Chinese PhD students. Of course, just supporting Estonian teenagers is not enough and copying the system to Latvia is not going to work as you’d loose all the mass pull effect of the established community while also risking getting the infectivity parameters wrong.

So there you go, one of the answers to MJ’s question “how do we detect things that are about to explode before we do so we can get filthy rich” is as follows. You look for things that are catering a local target group very well in a way that is scalable without copying. Colleges, kindergartens, office environments. Things like that.

One other thing that is clear from the model presented previously I did not point out is the lack of the concept of an “active user”. They do not matter. You might have hundred million people coming to your site to look at stuff but unless they actually create something provoking comment, begging for a “like” or asking for support in a mob war, there is not going to be another hundred mill.

So there’s a second answer to MJ’s question. Look for companies that do not track active users but track contributing users instead. Look for ways a company makes it easy to get infected without triggering the subject reaching for a face mask (very infectious diseases do not spread because they become known and the number of contacts goes down because of public awareness). Look for companies that understand that distinction.

Allright, that’s all for now. Take care and observe System Dynamics in Action!

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