Having put out a thread on why networks/heterogeneities often aren't needed in models, let me talk a little about cases where it does matter:
Right now a lot of places are on lockdown - this likely has a larger impact on the people with many contacts than on others.
People with many contacts are important - they are likely to get infected, and likely to infect others.
People with many contacts are important - they are likely to get infected, and likely to infect others.
As we reopen, it's not the average increase in degree that matters.
It turns out that R is proportionatl to the average square of the degree divided by the average degree.
So if average degree doubles, R could grow by a lot more.
It turns out that R is proportionatl to the average square of the degree divided by the average degree.
So if average degree doubles, R could grow by a lot more.
But we don't know enough to say how much more. This means we need to be very cautious as opening occurs.
Another effect we need to think about is degree-degree correlations. If someone's place in life puts them at high-risk it's likely that it also puts them in contact with other high-risk people. This means that we get small subgroups with much higher risk than average.
Think: meat packers (recent outbreak in Australia, many in the US), prisons, police officers, health care workers, people in long-term care facilities, the homeless, migrant workers.
These hot-spots exist and infection is very hard to control if it gets in.
These hot-spots exist and infection is very hard to control if it gets in.
So we need to take extra precautions in these places to keep it out and to respond aggressively if it's spotted in one, and to prevent spread between potential hotspots.
I'd advocate for reduced meat inspections right now.
Hospitals should have different sections set for COVID-19 patients, and the non-COVID-19 patients should be themselves subdivided into separate cohorts.
Hospitals should have different sections set for COVID-19 patients, and the non-COVID-19 patients should be themselves subdivided into separate cohorts.
Additionally, network theory is particularly relevant for thinking about contact tracing paradigms right now. Lots going on here, but I'm not qualified to comment.
So yes, there are good reasons to think about heterogeneity.
But it's complicated.
But it's complicated.
If you say: heterogeneity means we reach herd immunity sooner and so we can reopen safely now...
the counter argument is that if the population is heterogeneous, that means shutdowns are even more effective, so stopping a shutdown gives a large bump to R_eff.
the counter argument is that if the population is heterogeneous, that means shutdowns are even more effective, so stopping a shutdown gives a large bump to R_eff.
We are thinking about these things. I promise.
