Two stages, both grounded in real epidemiological models (identical math to the 3D version, viewed here from directly above as a flat contact map):
1. Spillover (dose-response). Each contact between the reservoir and a susceptible human exposes them to V independent virions, each with a small per-virion infection probability p that scales with receptor-binding affinity α (how well the pathogen's surface protein docks to the human cell receptor — e.g. Spike↔ACE2, or hemagglutinin↔sialic acid linkage). The independent-action hypothesis gives:
p ≈ 0.05 + 0.9·α (per-virion probability)
P(infection) = 1 − (1 − p)^V (dose-response)
2. Human-to-human branching process. A newly infected person sits in a contact network of degree k (the "distancing" slider). Each tick they infect each susceptible neighbour with rate β = 0.55·α and recover with rate γ = 0.35, giving reproduction number:
R₀ = (β / γ) · k
Extinction probability q solves: q = e^(R₀(q−1))
P(major outbreak) = 1 − q (for R₀ > 1, else ≈ 0)
q is solved each frame by fixed-point iteration on the generating function of a Poisson-offspring branching process — the same math used to explain why most spillovers (R₀ < 1, e.g. early avian H5N1 in humans) die out even though the pathogen is lethal, while a handful of spillovers with R₀ > 1 (1918 flu, SARS-CoV-2) ignite a pandemic. (Verified numerically in a scratch script: the iteration converges monotonically to the correct smallest root of q = e^(R0(q-1)) for every R0 the sliders can produce, from 0 up to ≈14.9 — the 3D source's formula and 60-iteration budget are both correct as written.)
- Contact rate — how often the reservoir and human population interact (wildlife markets, deforestation, farming).
- Receptor-binding affinity α — the molecular adaptation of the pathogen to the new host; raises both spillover probability and human R₀ at once, mirroring how a single mutation (e.g. HA Q226L) can do both.
- Exposure dose V — how much pathogen a contact transfers (raw contact, versus a single respiratory droplet).
- Network degree — human social contact density; lowering it is what "social distancing" does to R₀ in the formula above.
Drag to pan the contact map, scroll/pinch to zoom in on a chain of transmission beams.