[thaumasiotes]

If you kill all the mosquitoes (at any stage of life) in 2013, their 2014 population will remain zero, yes.

If you kill less than that, then the 2014 population will be determined by the environment of 2014, mostly without reference to 2013. I pointed out below your comment that if mosquitoes could reproduce merely as fast as the Irish between 1961 and 2011 (and in reality they do it much faster; a female human can't have more than about 15 children, whereas a female mosquito can easily lay several hundred eggs), and their generation length were one year, then they would recover fully from a blow much larger than the potato famine two years after such a blow occurred.

Having looked into it, I see that the actual generation length of mosquitoes ranges from several days (!) to one month. So with very high confidence, I can say that the effects of a raging mosquito genocide will not be felt by one year after it has concluded, unless ALL the mosquitoes in the area were successfully killed.

You might find http://www.straightdope.com/columns/read/21/if-i-hadnt-kille... to be of interest.