SIR Epidemic: Network vs Mean-Field Theory

S:   I:   R:
S (network)
I (network)
R (network)
S (MF)
I (MF)
R (MF)

Parameters

SIR model: S→I at rate β per infected neighbor; I→R at rate γ.

Mean-field ODE: dS/dt = −βkSI/N, dI/dt = βkSI/N − γI.

Epidemic threshold: R₀ = βk/γ > 1. Network heterogeneity causes deviations from mean-field predictions.