Schistosomiasis is a chronic inflammatory parasitic disease caused by multi-year infection with Schistosoma species trematodes spread in many tropical and sub-tropical regions of the world. Its control and elimination was advocated by World Health Organization in their 2020 Roadmap on Neglected Tropical Diseases, and by the 2012 London Declaration. However, effective control of schistosomiasis remains a challenging problem for populations at risk.Schistosoma parasites have a complex life cycle, alternating between human and snail hosts. We have developed new mathematical models to study schistosomiasis transmission and control, based on a stratified worm burden approach (SWB). The model accounts for in-host biology, snail ecology, host demographics, and diagnostic uncertainties. We developed a new calibration methodology for such models based on egg-count data and Bayesian statistics, with which one can incorporate uncertainties of the model and the data, and make statistical predictions on projected outcomes. We apply this model and calibration scheme to study control and elimination of schistosomiasis in several endemic regions of sub-Saharan Africa. We used different combinations of mass drug administration (MDA) inputs (control group, frequency and coverage) to attain a specific goal of elimination or targeted reduction. Repeated MDA of high frequency (annual or higher), degree of participation (>70% coverage), or a broader control group (community-wide vs. children) was shown to gain substantial reduction of infection. However, we also found that parasite reproduction and transmission were sufficiently robust to bring system back to pre-control level once MDA is suspended. So MDA alone is unlikely to interrupt transmission, and ultimately supplemental interventions (e.g. snail control, improvements in sanitation etc.) will be required to achieve full control of Schistosoma transmission.