⟨HERD IMMUNITY⟩

R₀: -
Herd immunity threshold: -
Vaccinated: -
Susceptible: -
Infected: -
Recovered: -
Final size: -
Herd immunity threshold (HIT) = 1 − 1/R₀ for homogeneous networks. For heterogeneous (scale-free) networks: HIT = 1 − ⟨k⟩/(⟨k²⟩/⟨k⟩ · R₀). High-degree hubs lower the effective HIT — target vaccination is critical. Observe how hubs seed and sustain outbreaks.