Epidemiological Modeling
Students explore mathematical models of disease transmission, including SIR/SEIR compartmental models, the basic reproduction number R0, and how indoor air quality interventions can reduce transmission in enclosed spaces.
5
Lessons
5
Class Periods
Low
Materials Cost
3
NGSS Standards
Essential Question
How can mathematical models help us understand and predict disease outbreaks, and how does improving indoor air quality reduce transmission?
Lessons
- 1→Introduction to SIR Models
- 2→The Basic Reproduction Number R0
- 3→SEIR and More Complex Models
- 4→Intervention Modeling
- 5→Outbreak Simulation Project
Key Concepts
SIR Model
- dS/dt = -beta*S*I/N
- dI/dt = beta*S*I/N - gamma*I
- dR/dt = gamma*I
- Susceptible, Infected, Recovered
R0 and Rt
- R0 = beta/gamma (basic reproduction number)
- Rt = R0 * S/N (effective reproduction number)
- Epidemic threshold: R0 > 1
- Herd immunity threshold: 1 - 1/R0
Wells-Riley Model
- P = 1 - exp(-Iqpt/Q)
- Airborne transmission probability
- Quanta emission and inhalation
- Ventilation as intervention
Intervention Effects
- Ventilation reduces transmission
- Filtration equivalent ventilation
- Masks reduce quanta emission/inhalation
- Combined interventions multiply
Standards Alignment
| Standard | Description |
|---|---|
| HS-LS2-1 | Use mathematical representations to support claims for the cycling of matter and flow of energy |
| HS-LS2-6 | Evaluate claims about group behavior, population density, and ecosystem disruption |
| HSF-IF.B.4 | For a function that models a relationship, interpret key features in terms of quantities |