So why does all this matter?

It matters because there are a number of implications of how disease spread that

turn out not to generalize to situations where behaviors spread.

So for instance, when we think about the spread of an innovation.

Innovation spread much more effectively in a small world, or

in a world with weak ties.

When those innovations are simple or

easy to adopt when they're costs less there's not a lot of risk involved.

However, when innovations are risky all of a sudden the networks that would help

the simple innovation spread slow down the spread of a difficult innovation.

More importantly, when we think about collective action or

recruitment to a new kind of social movement.

If it's an easy social movement, something like a neighborhood trash cleanup,

then people just really need to know where to go and when.

So it's just a matter of information diffusion and in that case,

small worlds would be better for organizing collective action.

However, if it's recruitment to something like Freedom Summer where there's a lot of

cost involved and it's extremely risky.

And that's a situation where small world networks will actually

slow down diffusion.

First of all because people need multiple sources of reinforcement to be convinced

to adopt.

But second of all because the riskier the innovation is the more the information

flow is a problem.

Particularly if you're trying to organize a revolution against,

say an oppressive government.

Then you actually don't want a lot of information flow,

you want it to be secret that you're doing this sort of thing.

And so you'd prefer networks that were more closed to a neighborhood effect that

ensure that people would trust the people they talk to.

And that the signals that came in were reliable.

And so these are all situations where complexity changes the diffusion dynamics

of a contagion.

Making it more likely to spread through clustered networks than through small

world networks.

One of the interesting things to think about from a modeling point of view when

we think about all these implications is what happens when the networks become more

realistic.

Or the assumptions move more from a modeling space into the real world.

Well, one of the things we can do in a model is explore some of these

assumptions.

So right now the models we've looked at have had thresholds of one or

thresholds of two.

But we can ask about threshold heterogeneity.

What if there's a distribution of thresholds?

Or what if thresholds are probabilistic so

people can change their decisions over time?

Moreover, instead of just looking at networks where everyone has the same

number of ties and ties are rewired.

What if there are hubs in the network?

Some people who are extremely well connected.

And other people have only a few ties.

Well, hubs are extremely effective for spreading information and

spreading disease.

As soon as a hub gets infected or gets a piece of information everyone the hub is

connected to gets the piece of information or gets infected.

Is it the same for a complex contagion?

Finally, we've been looking at adding ties as rewiring.

But what if you actually added ties to networks?

So increased the density.

There's more and more links in the network, and you introduced weak ties, and

made world small that way.

How would all of these differences affect the dynamics?

One of the useful things about modeling in this way is that we can ask all of these

questions, in fact we did.

It turns out that the threshold heterogeneity actually makes

the results stronger.

It turns out that when you put hubs into the network it actually makes it

harder to spread complex contagions.

And it turns out when you add ties to the network, for much of the same reason as

hubs, it actually also make it harder to spread complex contagions.

So in conclusion we can use the models to explore all these different robustness

assumptions.

And look at the variety of situations where changing the model and

introducing features that make it more realistic don't affect the diffusion

of complex contagions.

Interestingly find the very few cases where it does.