Correction: Wells–Riley Model & Coronavirus/Rhinovirus Dose–Response
- The mathematical models used to assess the risk of airborne viral infections, like those experienced during the COVID-19 pandemic, are under ongoing scrutiny.
- Predicting the probability of infection from airborne viruses is a complex undertaking.
- During the COVID-19 pandemic, a modified version of the one-parameter exponential model – essentially the Wells-Riley model – became the primary tool for assessing infection risk.
The mathematical models used to assess the risk of airborne viral infections, like those experienced during the COVID-19 pandemic, are under ongoing scrutiny. A recent study, with a correction published on , revisits the widely used Wells-Riley model and compares its performance against other dose-response models in the context of human respiratory viruses.
Understanding Airborne Infection Risk
Predicting the probability of infection from airborne viruses is a complex undertaking. It requires understanding how many viral particles a person is exposed to, how infectious those particles are and the individual’s susceptibility. Early attempts to quantify this risk relied on the concept of the “quantum” or “quanta,” initially proposed by William F. Wells, to account for the unknown infectious dose needed to cause infection. The Wells-Riley model, developed by Edward Riley and colleagues, utilizes this concept to estimate infection transmission risk.
During the COVID-19 pandemic, a modified version of the one-parameter exponential model – essentially the Wells-Riley model – became the primary tool for assessing infection risk. This was largely due to its relative simplicity and the availability of data from animal studies susceptible to SARS-CoV. However, researchers have long recognized that differences exist in susceptibility between animals and humans, prompting a continued search for more accurate models.
The Exponential Model vs. Alternatives
The two most commonly used dose-response models for calculating infection risk are the exponential model (Wells-Riley) and the Stirling approximated β-Poisson (BP) model. While the two-parameter Stirling BP model is often recommended for its flexibility, it has limitations. The Stirling approximation relies on specific conditions – β being much greater than 1 and α being much smaller than β – which are frequently not met in real-world scenarios. This can compromise the model’s accuracy.
To address these limitations, researchers have explored alternative approaches to the BP model, utilizing the Laplace approximation of the Kummer hypergeometric function instead of the more conservative Stirling approximation. This novel BP model aims to provide a more robust and reliable assessment of infection risk without the restrictive conditions of the traditional Stirling approximation.
Comparing Model Performance with Human Data
The recent research directly compared the performance of four dose-response models – the exponential model, the traditional Stirling BP model, and two variations of the BP model (including the novel Laplace approximation version) – using datasets of human respiratory airborne viruses. Specifically, the study focused on human coronavirus (HCoV-229E) and human rhinovirus (HRV-16 and HRV-39).
The findings revealed that, based on goodness-of-fit criteria, the exponential model – the Wells-Riley model – actually provided the best fit for both the HCoV-229E and HRV-39 datasets. This suggests that, despite its simplicity and the availability of more complex alternatives, the Wells-Riley model remains a valuable tool for assessing infection risk in these specific cases.
Implications for Public Health and Future Research
The study’s findings have important implications for public health risk assessments. While more sophisticated models exist, the exponential Wells-Riley model offers a practical and reasonably accurate approach, particularly when data are limited. This is crucial for rapid response scenarios, such as the early stages of a pandemic, where timely risk assessments are essential.
However, it’s important to note that the “best” model can vary depending on the specific virus, environmental conditions, and population being studied. The researchers emphasize the need for continued investigation into the strengths and weaknesses of different dose-response models to refine our understanding of airborne infection transmission. Further research is needed to determine the optimal model for a wider range of respiratory viruses and real-world settings.
The correction highlights the ongoing refinement of epidemiological models used to understand and mitigate the spread of respiratory illnesses. The continued evaluation of these models, using robust human data, is critical for informing public health strategies and protecting populations from future outbreaks.