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Background: The dynamic interactions of severe infectious diseases with epidemic potential and their hosts are complex. Therefore, it remains uncertain if a sporadic zoonosis restricted to a certain area will become a global pandemic or something in between. Objective: The objective of the study was to present a surveillance system for acute severe infections with epidemic potential based on a deterministic-stochastic model, the StochCum Method. Design: The StochCum Method is founded on clinical, administrative, and sociodemographic variables that provide a space/time map as a preventive warning of possible outbreaks of severe infections that can be complemented based on the sum of all the first accumulated cases. If the outbreak is happening in high-risk areas, an early warning can be elicited to activate the health response system and save time while waiting for the confirmation of symptomatic cases. Results: The surveillance system was tested virtually for 1 month on admissions to the emergency room of a public hospital located in Mexico City, Mexico. It promptly identified simulated cases of acute respiratory infections with epidemic potential. Conclusions: The StochCum Method proved to be a practical and useful system for conducting epidemic surveillance on a hospital network.