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For your record: If human population on Earth exceed 10 billions, planet will be overpopulated - 30% of humans could then die because of overpopulation. Even now, 6 billions is problematic number - many people is dying because they don't have fresh water, food or because of illness (bigger population - easier to get sick).
I also think that 200 millions would be postwar population of Earth. Covies attacked every city on Earth, even 2-3 months of that kind of attack would be destructive.
UNSC was able to win most on ground engagements, but not if Covies had support from air and space. Even if in some areas humans won, Covies for sure would glass that area.
BTW. Covies were at Earth from 20 October 2552 to 3 March 2553. It gives 5-6 months. How much time Covies would need to eradicate human population on planet? Well, whole H-C war lasted for 27 years to compare.
I think, that up to 60% of humans were eradicated during that war.
According to Cortana: http://halo.wikia.com/wiki/Human (see Population)
Before the war human population was at level of aprox.39 billions. During H-C war aprox.23 billions were killed. When you add birth rate to those calculations - after war remained aprox. 20 billions of humans. When Reach was recolonized human population was at level of aprox.24 billions.
[Edited on 07.02.2011 3:51 PM PDT]