Prosecuting traffickers reduces supply, not demand. The only way to reduce demand is to reduce the number of people who want to pay for sex, which is kind of tricky. You reduce supply without affecting demand and all that happens is the price goes up. Then someone else appears to take advantage of the high price and the market stabilises again. It's pretty fundamental stuff.
The problem of course is that as long as the demand persists, there will be somebody willing to supply to it. That's just basic economics. You can prosecute every pimp/trafficker you can get your hands on, you're just playing whack-a-mole until you can figure out a way to mitigate the demand to the point where there's no real money to be made meeting that demand. Whether that's by legalising prostitution, education in why illegal prostitution almost inevitably leads to the exploitation of young women or much worse, or some other means of stopping people wanting to pay for sex.
Saying "we'll arrest all the traffickers" is a very good thing insofar as it punishes nasty people for doing horrible things but it's no long term solution to prostitution. We've had prostitution as long as we'd have an economy to speak of (i.e. since there was a way to exchange something of value for the service provided) and we probably always will, it's more a question of how you manage it so fewest people get least hurt.
