OASIS describes OA business models and provides case studies

By scanning the Social Sciences subject areas in the DOAJ one can see which and how many of the included journals have front-end publication fees.  The table below reflects an approximation:

SHERPA/RoMEO lists Pusblisher's paid OA option - Publishers' paid open access options, allow authors to deposit their articles immediately in open access repositories upon payment of a fee. The same publishers may also allow authors to deposit after an embargo period without payment of a fee.

Where a publishers' standard policy does not allow an author to comply with their funding agency's mandate (see JULIET), paid open access options may enable an author to comply