The cluster model of ultraviolet disinfection explains tailing kinetics

To develop a new mathematical model derived from first principles to define the kinetics of ultraviolet disinfection and to explain the phenomenon known as tailing. The theory presented interprets tailing as the result of photoprotection due to cumulative Mie scattering effects in clustered populations of micro-organisms.

Mie scattering effects at ultraviolet wavelengths are used to compute a shielding constant for each micro-organism based on the average projected diameter. An intrinsic rate constant, hypothesized to be a characteristic property of the microbial genome alone, is computed. The cluster model is fitted to tailing data from 30 ultraviolet inactivation studies and results are compared with the classic two stage multihit model.

The cluster model demonstrates a statistically significant improvement in the mean adjusted R² values of the tested data sets (P < 0·0001). Tailing in survival curves is the direct consequence of the Gaussian distribution of cluster sizes and the intrinsic rate constant is a real and critical parameter that defines ultraviolet susceptibility.

The ultraviolet dose-response behaviour of micro-organisms can now be explained in terms of parameters that have physical meaning and provide deep insight into the disinfection process.