Complex biological systems pose many challenges to researchers, including, inter alia, choice of computational model, with its consequences for simulation and analysis; methods of manipulating the system exogenously (control); and model validation. I attempt to address these issues for human blood clotting. By treating the system as comprising interacting discrete and continuous aspects, i.e. as hybrid, the entire coagulation cascade may be simulated: Blood proteins, elemental ions, and other state elements are modeled either as real-valued concentrations or as binary variables (present/absent); interactions are rendered either as ODEs (per their chemical equations) or as discrete events. Techniques from nonlinear control theory are then used to devise drug therapies for diseased patients. Finally, the model is used to warp variations in the input parameters --- rate constants and initial conditions --- into an output space where pathologies and healthy clotting are cleanly separated by a semi-supervised clustering analysis. This serves to validate the model as well as to summarize efficiently the predicted clinical consequences of individual variations.