An article just quoted an estimate for the number of Islamic State fighters in and around Mosul: Retaking Mosul
They estimate that “IS fighters in Mosul, meanwhile, vary from a few thousand to “not more than 10,000.” according to the coalition.”
They also note that the current population of Mosul is estimated at between 500,000 and one million. Also: “Al-Hashimi, the analyst, estimated retaking Mosul would require 80,000 men, of whom 15,000 are expected to come from the government-sanctioned Shiite militias.’
Also note: “An official…said there was not yet a detailed plan for retaking Mosul. “for now, the plan is simply that Mosul is next.'”
Anyhow, estimating the size of an insurgency or irregular force is somewhat of a challenge. Part of the challenge is that a significant percent (the majority?) of the force and the support personnel for the force is not “full-time”….so to say. They are people that are activated irregularly and as needed. I ended up with an entire chapter in my book America’s Modern Wars on estimating insurgent force size. In the end, I concluded that you are probably best estimating the force size based upon their levels of activity (incidents occurred and people killed) compared to other insurgencies. This did produce estimates higher than the official U.S. DOD estimates for Iraq and Afghanistan. In retrospect, it appear our estimates were closer to reality.
Of course, all these “part-time” and “casual” insurgents disappear back into the population when you occupy an area and are available to be called upon again.