Deterministic modeling of infection dynamics under Far-UVC irradiation: a cumulative-exposure framework and its mathematical relation to infectious quanta

Far-UVC irradiation (200–235 nm) is a promising photonic intervention for suppressing the environmental transmission of airborne pathogens in occupied spaces. However, establishing a robust physical and mathematical framework to quantify these dynamic pathogen-host interactions remains challenging, as direct verification using mammalian models is experimentally demanding and cost-prohibitive. Here, we present a controlled in vivo biophysical model system—utilizing zebrafish and Yersinia ruckeri —to quantitatively examine the macroscopic survival dynamics of a host population under varying environmental pathogen loads. We observed a distinct, threshold-like transition in macroscopic host survival near a critical pathogen density (10 6 CFU/mL for a 0.25-day exposure duration), above which infection-induced mortality sharply increased. Far-UVC irradiation reduced the viable pathogen density as a function of UV dose, systematically driving the system below this critical threshold and demonstrating effective physical pathogen attenuation. To elucidate the underlying dynamics, we introduced a deterministic, multistep Susceptible-Infectious-Removed (SIR) model governed by a system of coupled differential equations. The theoretical model revealed that the final macroscopic state of the system is governed by a cumulative exposure parameter, Λ = β 0 ρτ , where β 0 is the infectivity coefficient, ρ is the bacterial density, and τ is the exposure duration, rather than by instantaneous bacterial density alone. Crucially, the cumulative exposure parameter Λ derived from this aquatic infection model shares the same exponential cumulative form with the infectious quanta in the Wells-Riley model for predicting airborne transmission. Therefore, this in vivo platform validates a quantitative physical framework specifically for evaluating ultraviolet (UV) disinfection dynamics. These findings provide a theoretical basis for designing precise photonic irradiation algorithms that maintain cumulative environmental exposure below critical pathogenic thresholds.