Endemic SIR Model
Disease persistence and endemic equilibria with birth/death vital dynamics
Susceptible (S)
Infected (I)
Recovered (R)
Endemic equilibrium
Parameters
Transmission rate β:
0.30
Recovery rate γ:
0.10
Birth/death rate μ:
0.01
Restart
Statistics
R₀
—
Endemic S*
—
Endemic I*
—
Herd immunity threshold
—
With vital dynamics (births = deaths = μ), a disease can persist as endemic if R₀ > 1. The endemic equilibrium is S* = 1/R₀, I* = μ(R₀−1)/(β).