Seismicity associated with subsurface operations is a major societal concern. It is therefore critical to improve predictions of the induced seismic hazard. Current statistical approaches account for the physics of pore pressure increase only. Here, we present a novel mathematical model that generalises adopted statistics for use in arbitrary injection/production protocols and applies to arbitrary physical processes. In our model, seismicity is driven by a normalised integral over the spatial reservoir volume of induced variations in frictional Coulomb stress, which—combined with the seismogenic index—provides a dimensionless proxy of the induced seismic hazard. Our model incorporates the classical pressure diffusion based and poroelastic seismogenic index models as special cases. Applying our approach to modeling geothermal systems, we find that seismicity rates are sensitive to imposed fluid-pressure rates, temperature variations, and tectonic conditions. We further demonstrate that a controlled injection protocol can decrease the induced seismic risk and that thermo-poroelastic stress transfer results in a larger spatial seismic footprint and in higher-magnitude events than does direct pore pressure impact for the same amount of injected volume and hydraulic energy. Our results, validated against field observations, showcase the relevance of the novel approach to forecast seismic hazards induced by subsurface activities.