Depending on the focus of your paper, you could try the BMC series (Infectious Diseases, Microbiology, Public Health etc) or the Malaria Journal. They all are free, and some have impressive impact factors.
For any research, in order to be published fast, it should be well conducted and well written; this will help the reviewers to complete the peer review process early and this will consequently will help the editors to take the decision for publication early . Regarding the other aspect of your question (for free publication), try with: travel medicine, journal of travel medicine and infectious diseases, Asian Pacific Journal of Tropical Medicine, annals of Saudi medicine, Scandinavian Journal of Infectious Diseases. All are free with good impact factors.