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Your Universe of Digital Possibilities
One node catches it. Each tick, it infects susceptible neighbours with probability β and recovers with probability γ, and the ember either dies in a corner or races the whole graph — decided by R₀, the number of new cases each case makes. The twist is the network: the same β and γ crawl across a geometric mesh, jump a small-world ring, and explode through a scale-free hub. And vaccinating just enough — 1 − 1/R₀ — kills it without immunising everyone, because an epidemic is percolation set in motion.
The classical well-mixed model: susceptibles become infected in proportion to contacts between S and I, and infecteds recover at rate γ. The whole epidemic is a flow S → I → R.
The single most important number in epidemiology: the average number of new infections one case produces in a fully susceptible population. Above 1 the outbreak grows; below 1 it dies.
On a contact network the right number uses the excess degree — who your neighbours’ neighbours are. A heavy-tailed (scale-free) degree distribution makes ⟨k²⟩ blow up, so hubs push R₀ far above the well-mixed estimate.
Immunise a fraction p and you thin the network of usable paths. Past p_c the infected component can no longer span the graph and the outbreak stops — even though a majority remain susceptible.
The deep identity: an outbreak is the giant connected component of “occupied” edges, each present with probability T. Vaccination is site percolation; transmissibility is bond percolation. The epidemic threshold is a percolation threshold.
On scale-free networks the threshold can vanish entirely: with a diverging ⟨k²⟩ any transmissibility spreads. The cure is not more vaccine but smarter targeting — immunise the hubs and the giant component shatters.
This is the rack’s network-dynamics instrument — the same law given three bodies and asked to spread. It is the moving twin of The Percolation (INST·26): there, connectivity appears as you fill a static lattice; here, it is walked in real time by a contagion, and vaccinating is exactly thinning that lattice below its critical point. It shares its threshold-at-R₀-=-1 with The Threshold (INST·04) and its agent-level emergence with The Flock(INST·10). And it is the literal picture behind the profile’s claim that everything is a system: epidemics, rumours, bank failures, blackouts and viral posts are one mathematics, and what decides their fate is less the pathogen than the shape of the graphit travels — the Perception Engine’s task of seeing the structure under the signal.