The SIR model divides a population into Susceptible, Infected, and Recovered compartments.
Model Equations
- dS/dt = -βSI/N
- dI/dt = βSI/N - γI
- dR/dt = γI
Key Parameters
- β (beta): Transmission rate
- γ (gamma): Recovery rate (1/infectious period)
- R₀ = β/γ: Basic reproduction number
Epidemic Threshold
An epidemic occurs only if R₀ > 1. Herd immunity threshold = 1 - 1/R₀.