Intervention Modeling
Learning Objectives
- Apply the Wells-Riley model for airborne transmission
- Calculate infection probability based on ventilation rates
- Model the effect of masks on transmission
- Compare effectiveness of different interventions
- Combine multiple interventions in layered protection
The Wells-Riley Equation
P = 1 - exp(-Iqpt/Q)
- P: Probability of infection
- I: Number of infectious individuals
- q: Quanta emission rate (infectious doses/hour)
- p: Breathing rate (m3/hour)
- t: Exposure time (hours)
- Q: Ventilation rate (m3/hour)
How Interventions Reduce Transmission
| Intervention | Effect in Model | Typical Reduction |
|---|---|---|
| Ventilation | Increases Q | Proportional to ACH increase |
| HEPA filtration | Adds equivalent Q | CADR added to Q |
| Source mask | Reduces q | 50-90% reduction |
| Recipient mask | Reduces p (effective) | 50-90% reduction |
| Reduced time | Decreases t | Proportional |
Layered Protection
When interventions are independent, their effects multiply:
Overall risk = Base risk x (1-eff1) x (1-eff2) x (1-eff3)
Example: 80% effective ventilation + 70% effective masks + 50% effective time reduction:
Risk = Base x 0.2 x 0.3 x 0.5 = 3% of baseline
Activity: Classroom Safety Analysis
A classroom has: Volume = 200 m3, 25 students, 1 teacher, ACH = 2, t = 6 hours
Assume one infectious person with q = 50 quanta/hour, p = 0.5 m3/hour
- Calculate the probability of infection for a susceptible student
- What ACH would reduce risk by 50%?
- If HEPA filters add 5 eACH, what is the new risk?
- If everyone wears masks reducing emissions and inhalation by 70% each, what is the combined risk?
Key Takeaway
The Wells-Riley model provides a quantitative framework for understanding airborne transmission and evaluating interventions. Ventilation, filtration, and masks all reduce transmission probability, and their effects combine multiplicatively. This analysis shows why layered protection is so effective for reducing indoor transmission risk.