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Engage
Introduction to SIR Models
Learning Objectives
- Define the three compartments of the SIR model (Susceptible, Infected, Recovered)
- Write and interpret the differential equations governing SIR dynamics
- Explain the meaning of transmission rate (beta) and recovery rate (gamma)
- Simulate SIR dynamics using spreadsheet models
- Interpret epidemic curves and identify key features
The SIR Model Framework
The SIR model divides a population into three compartments:
S - Susceptible
Can catch the disease
I - Infected
Currently infectious
R - Recovered
Immune (or deceased)
The Differential Equations
dS/dt = -beta * S * I / N
dI/dt = beta * S * I / N - gamma * I
dR/dt = gamma * I
Where:
- beta = transmission rate (contacts per time x probability per contact)
- gamma = recovery rate (1/infectious period)
- N = total population (S + I + R, constant)
Activity: Simulating an Outbreak
Spreadsheet Simulation
Build an SIR model with: N = 1000, I(0) = 1, beta = 0.3/day, gamma = 0.1/day
- Set up columns for time, S, I, R
- Use Euler's method: S(t+dt) = S(t) + dS/dt * dt
- Plot all three curves over 100 days
- Calculate peak infection time and size
- Experiment with different beta and gamma values
Key Takeaway
The SIR model provides a mathematical framework for understanding epidemic dynamics. The interaction between susceptible and infected populations, governed by transmission and recovery rates, produces the characteristic epidemic curve. This foundation will allow us to explore R0 and intervention modeling in subsequent lessons.