It will be exceedingly difficult to slow down the international sex trade. The reason for this is that this trade probably cannot be slowed down significantly through laws. It, like the trade in illegal drugs, is something that seems to be very difficult to combat legally. Instead, the international sex trade (like the sex trade within a country) is something that can only be combatted by seriously reshaping the economy and the society.
The sex trade exists for two main reasons. First, men see women as sex objects and are willing to pay to get the kind of sex that they want. Unless men’s views of women and their willingness to pay for sex are changed, they will continue to pursue prostitutes. Second, the sex trade exists because women need the money and cannot get it in other ways. This can be combatted by creating an economy that is good enough that it provides a lot of jobs that pay women well enough to allow them to avoid prostitution. It can also be combatted by making sure that all women have the education and skills needed to get good jobs.
Clearly, both of these tasks are massively difficult. Therefore, it will be very difficult to seriously slow down the international sex trade in any way that we are likely to be willing to do (it might work to give extremely harsh punishments to the men involved, but this is unlikely to happen).