Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, , and provide the governing PDEs for . This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order( p ) allows balancing accuracy and computational cost, providing a speedup of over N/p compared to high-fidelity models. Using a simplified coagulation network and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. These models depart from the high-fidelity solution by under 16% ( p = 1) and 5% ( p = 2) after 20 cardiac cycles. The favorable accuracy and low computational cost of multi-fidelity models could enable unprecedented coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it can be generalized to advance our understanding of other systems biology networks affected by blood flow.