The Wells-Riley Model Revisited II: Parameter Uncertainty and Population Heterogeneity

Area of Science:

• Epidemiology
• Public Health
• Mathematical Modeling

Background:

• The Wells-Riley model is a standard tool for estimating airborne infection risk in indoor environments.
• Previous models often assume fixed parameters, neglecting real-world variability.
• Quantifying infection risk requires accounting for stochasticity in parameters like quanta generation and ventilation rates.

Purpose of the Study:

• To extend the Wells-Riley model into a probabilistic framework to quantify airborne infection risk.
• To analyze the impact of parameter uncertainty on infection risk calculations.
• To provide a comprehensive analytical quantification of uncertainty in infection risk assessments.

Main Methods:

• Developed a stochastic (probabilistic) framework for the Wells-Riley model.
• Treated key model parameters (quanta generation rate, ventilation rate, duration, infector number) as random variables.
• Computed the probability density function of the per-capita infection risk.

Main Results:

• The per-capita infection risk becomes a random variable between 0 and 1 when parameters are uncertain.
• Uncertainty in quanta generation rate, duration, or infector number leads to infection risk overestimation.
• Environmental stochasticity (uncertainty in ventilation/removal rates) can lead to infection risk underestimation.

Conclusions:

• Using mean parameter values in the classical Wells-Riley model can cause systematic inaccuracies in risk assessment.
• The variability and distribution of model parameters significantly influence infection risk.
• Accurate infection risk assessment necessitates incorporating parameter uncertainty and stochasticity.