Galton-Watson branching process — R₀, extinction probability, outbreak size distribution
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Galton-Watson Process: Zₙ₊₁ = Σᵢ₌₁^Zₙ ξᵢ, ξᵢ ~ offspring distribution with mean R₀.
Extinction probability q satisfies q = G(q) where G is the PGF. For R₀ < 1 (subcritical): q = 1.
For R₀ > 1 (supercritical): q < 1, given by smallest fixed point of G. Overdispersion (NB) increases extinction probability even when R₀ > 1.