HIV remains a serious public health problem in many marginalized communities. We develop a network model of the HIV epidemic affecting injection drug users and female sex workers in the Downtown Eastside neighborhood of Vancouver, Canada, calibrated using data from public health surveillance and cohort studies. Many HIV positive individuals are unaware of their status and strategies for testing are an important part of HIV response programs. Upon diagnosis, HIV patients enter a continuum of care, involving both engagement and retention in treatment. We explored potential epidemic control strategies through simulation: reduced syringe sharing during injection drug use, reduced time to diagnosis, reduced time to initiation of treatment following diagnosis, and improved retention in treatment. We find that syringe sharing, HIV testing, and retention in treatment significantly impact HIV prevalence. Close connections between syringe sharing and sexual networks deserve attention as important avenues for rapid HIV transmission.