Universal Epidemic Scaling: Influenza And COVID-19

Conventional compartmental models may become difficult to parameterize over multi-wave epidemic horizons when susceptibility and transmission conditions change between successive epidemic regimes. This study introduces a reduced macroscopic framework that changes the scale of epidemic description from individual-level transmission structure to effective population-level dynamics. Epidemic waves are formulated as transport processes governed by deterministic boundaries, mass balance, and a small set of effective macroscopic parameters. The susceptible population is represented by a dynamic Effective Susceptible Pool that can be re-initialized at transitions between biologically distinct epidemic regimes, while transmission resistance and external control measures are incorporated at the macroscopic level. The resulting equations admit a dimensionless similarity representation and closed-form analytical solutions, enabling analytical estimation of epidemic trajectories and peak healthcare demand without computationally intensive numerical simulation. The framework is evaluated using comparative time-series data for SARS-CoV-2 and seasonal influenza A within the geographically and demographically consistent setting of Rhode Island. Despite their different biological and immunological regimes, the analyzed trajectories exhibit a common reduced asymptotic scaling form. The results support the use of a macroscopic, scale-reduced representation for cross-calibration of heterogeneous surveillance signals and analytical assessment of healthcare-system demand. Further validation across pathogens, populations, and open-system settings is required.