The interesting question in stopping them is why do people choose to follow them?

Attacking them for their poor justifications will not help you get anything done. Ensuring nobody WANTS to help them is how you stop them. And to do that, you need to make sure people don't feel that extremely desperate and make sure they don't have a reason to blame your for their situation - because the people joining them feel that it is their best choice for improving their situation.

Give people there a better choice and ISIS will lose their power.

They follow out of religious devotion:

https://news.vice.com/video/the-islamic-state-full-length

(9:57 into the video)

Passenger: "We are fighters."

Driver: "I swear, we hope for hardship. We don't want a happy life and trips, the opposite, such things take us away from God. The harder the situation is, the closer we are to God."

And again, what drove them to take that position?

For the past century, the most important question asked by people in the middle east has been, "Why does the West have so much, and we have so little? Why are we always defeated politically, unable to rise to the stature of the West in every way?"

In the decades the followed the fall of the Ottoman empire), Arab nationalism ascended, and it answered this question with, "socialism and the formation of mighty nation-states will allow us to gain parity with the West materially, and then surpass it". For a multitude of reasons, this movement delivered neither military success nor material prosperity and became increasingly abandoned following the humiliation of the Six-Day War in 1967.

The replacement for Arab nationalism was a sharp turn toward religion on every topic, and in every aspect of life. The question became, "the West has material prosperity, but that is fleeting and an affront to God. furthermore it is no replacement for the riches of the hereafter."

This shift was no random accident - in fact, it was decades in the making prior to 1967. For more on that, read about the life and times of Sayyid Qutb. Prior to his death in 1966, he played a crucial intellectual role in shaping the Muslim Brotherhood.

An account of these shifts defies explanation in simple economic and/or material terms. Crises serve only to create gaps for whatever ideology has already taken root to rise to the fore. Ideology itself, that is, answers to pressing questions of the day, and coherent, integrated views of the world (even if they are wrong), is what ultimately drives all historical events, not the other way around.

Sounds to me like a case of not understanding the true cause leading to a case of The Fox and The Grapes (I can't achieve that, so I decide it is bad), leading to animosity. And then they justified that animosity by mixing it into their beliefs (religion - but one can argue the religion isn't a necessary component, just look at totalitarian communist regimes). Yes, probably oversimplified, but I still just see known common psychological traits in action.

I'll take a look at your references later.

Yes, ideology drives the direction. I'm very well aware of that and agree fully. But which one spread and how they spread and how popular they bevome largely depends on factors like, timing, who it spreads to first (influential people or not), the prior context, etc... Different contexts make it more likely for some ideas to spread but not others. Comparisons to virology is actually very applicable.

And a crisis is a typical situation that amplifies the probability of some idea spreading broadly and taking root, and the context and circumstances is part of influencing which ones.