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lecture14

# Set 1 recall is infection rate is recovery the time

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Unformatted text preview: eterogeneous thresholds seem to enhance global cascades. • Heterogeneous node degrees seem to reduce global cascades. Part I. C. Master Equation approaches • SIS and SIR dynamics on networks • Rather then thresholds, each infected neighbor has a probability of infecting a healthy Following Pastor-Satorras and A. Vespignani • ρk (t) is density of infected nodes of degree k at time t. (Hence [1 − ρk (t)] is probability a node of degree k is NOT infected.) • λ = β/γ , the effective spreading rate. Set γ = 1. (Recall β is infection rate, γ is recovery.) • The time evolution (a “master equation”): dρk (t) = −ρk (t) + λk [1 − ρk (t)] Θ(ρ(t)) dt • First term: nodes recover with unit rate (γ = 1) • Second term: Infection rate λ, times number of neighbors k , times prob node of degree k is healthy, times prob of being connected to an infected node Θ(ρ(t)). Searching for more solutions to last equation, in interval 0 < Θ ≤ 1 • Taking derivative w.r.t....
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