Results of the epidemiological measurement of endemics, epidemics, and pandemics

Reliable characterization of infection dynamics is critical for managing endemic, epidemic, and pandemic outbreaks. A persistent challenge in epidemiology is the lack of a unified quantitative framework that allows wave patterns to be compared across outbreak scales and pathogens while accounting for possible ambiguities in wave definitions. This study presents a descriptive epidemiological framework to quantify epidemic wave characteristics using the Duty Cycle (DC), defined as the ratio between wave duration and the time to the next peak. Historical time-series data from viral outbreaks were analyzed, and combinatorics was applied to consider all valid interpretations ("perspectives") of wave boundaries within the same incidence curves, thereby avoiding a perspective-selection bias. We calculated DC values, wave peak postdiction accuracy in days, wave heights relative to initial peaks, and subsequent wave frequencies. Distribution-based analyses show that DC values are generally higher in endemics and epidemics, indicating frequent overlapping waves, whereas pandemics tend to exhibit lower DC and fewer subsequent waves. Wave-peak postdiction accuracy varied across outbreak scales, with distributions reflecting perspective-dependent uncertainty. While subsequent waves of infection in endemics and epidemics are frequently higher than the first wave, pandemics typically peaked in the second wave and showed waning thereafter. The results provide a comparative, structurally grounded description of epidemic wave dynamics across outbreak types, supporting outbreak assessment and planning. Given the heterogeneity of reporting and outbreak dynamics, results should be interpreted as descriptive benchmarks rather than mechanistic postdictions.