SIR Information Epidemic (Kermack–McKendrick, 1927)

The epidemiological SIR model, borrowed to describe how an idea spreads: people move Susceptible → Infected (aware/sharing) → Recovered (saturated, no longer spreading).

dS/dt = −β·S·I, dI/dt = β·S·I − γ·I, dR/dt = γ·I, with S + I + R = 1. Here β is the transmission rate (contact × probability a contact "catches" and re-shares) and γ is the recovery rate (how fast a sharer goes quiet). The controlling number is the basic reproduction number R₀ = β/γ: the average people one sharer infects while active. R₀ > 1 → an outbreak that grows before it burns out; R₀ < 1 → it fizzles. The final size infected solves R∞ = 1 − e^(−R₀·R∞).

Transfer: Unlike the viral coefficient (a per-user ratio), SIR forces you to model γ — how fast the topic goes stale. Reach is β/γ, so halving the decay rate (staying re-shareable for two days instead of one) doubles R₀ as surely as doubling transmission. It also predicts burnout: S is finite, so a piece exhausts its susceptible pool and dies regardless of quality — an agent flooding one audience drives their S → 0 and future posts land on the recovered. The lever is fresh susceptibles (new sub-communities) and slower γ (evergreen framing), not just louder β.

Kin: bass-diffusion-model · viral-coefficient · tipping-point-critical-mass · models