I can give many citations, but they're also an easily Googled matter of public record. I'll provide some anyway.

On current events:

https://www.spectator.co.uk/article/six-questions-that-neil-...

https://judithcurry.com/2020/04/01/imperial-college-uk-covid...

https://twitter.com/AlexBerenson/status/1245748387359711234

https://medium.com/@wpegden/a-call-to-honesty-in-pandemic-mo...

On a major prior disaster caused by listening to Imperial modellers:

https://www.researchgate.net/publication/51683518_Destructiv...

https://journals.plos.org/plosone/article/file?id=10.1371/jo...

http://pdfs.semanticscholar.org/5ab5/c0d4699e499e9c99a20c8d7...

https://www.telegraph.co.uk/news/2020/03/28/neil-ferguson-sc...

Here they are getting it all wrong on Zika:

https://science.sciencemag.org/content/sci/353/6297/353.full...

https://www.sciencemag.org/news/2017/08/zika-has-all-disappe...

And finally, a page with many useful links under "further reading":

https://lockdownsceptics.org/how-reliable-is-imperial-colleg...

I hope that provides some interesting reading!

Is the fact that it's undocumented even relevant?

Absolutely. Ferguson asserted he couldn't reveal his code because nobody except him knows how to run it. That means nothing based on it could have ever been properly peer reviewed in 13 years. Over a month later he still hasn't uploaded his code anywhere, despite its outputs driving extreme social policies around the world. That's pathetic and deserves condemnation from anyone who cares about the scientific method. Being able to peer review and reproduce published results is critical - look at what happened in psychology when people tried to replicate famous papers - but this is one more way epidemiology doesn't even try to be scientific.

Does the spread of the virus differ other than in the sense of tweaking variables like R0? ... It's not immediately clear why a model originally developed for flu would not be readily adaptable to COVID-19

Nobody knows, do they. If anyone understood these viruses their models wouldn't always be so wrong. We can easily assert that here because on this forum we have nothing to lose.

At any rate, R0 and friends are the variables that define spread in these models. There don't seem to be fundamentally different models for different diseases. For instance SEIR models don't have any variable for different categories of disease and they aren't labelled as for use only with e.g. respiratory infections. Take a look for yourself:

https://en.wikipedia.org/wiki/Compartmental_models_in_epidem...

All viruses are treated the same same except for the initial starting variables. You can't exclude them whilst still asking if the spread of the virus differs in these models - the answer is no, but the models are wrong so that doesn't mean much about the real world.

It doesn't require detailed medical or virological knowledge either - just empirical observation, of which epidemiologists are quite capable.

That would require leaving their universities. The Imperial paper isn't based on fieldwork but second hand anecdotes (e.g. "Professor Nicholas Hart, personal communication" is cited as a source) and arbitrary guesses:

"We assume that symptomatic individuals are 50% more infectious than asymptomatic individuals"

This assumption is justified nowhere. It's for sure not based on empirical observation by the team.

BTW, let me ask you: do you consider economics a science?

No, of course not. As you note, economics has all the same problems as epidemiology. The public knows this and polls show economists aren't trusted. People have clocked that economists can't predict the economy even though they routinely claim otherwise. I hope epidemiology goes the same way quickly.

it seems like your opposition to epidemiologists' conclusions seems to be based in economic projections

I haven't mentioned economic projections anywhere in this thread. My opposition to their conclusions is based on the fact that they are treated as scientific when in reality they aren't. That this has led to economic disaster makes it a very important topic, but I can easily make the same case about less disastrous fields like nutrition 'science' or psychology. And if you browse my comment history (pre COVID), you'll see I have. COVID is also a social disaster, look at all the stories of the cops going full 1984 to see that.