The 80/20 Rule of Epidemics
Not all infected individuals are equal transmitters. For many respiratory pathogens, a small fraction of cases generates the vast majority of secondary infections. Studies of SARS-CoV-2 suggest that roughly 10-20% of cases cause 80% of all transmission, while 70-80% of infected people transmit to nobody at all. This phenomenon, called overdispersion, fundamentally changes how we should think about epidemic control.
The Dispersion Parameter k
The dispersion parameter k quantifies this heterogeneity. When secondary infections follow a negative binomial distribution with mean R₀ and dispersion k, lower k means more variation. At k = 0.1, the distribution has a long right tail — most cases produce zero secondary infections, but rare superspreading events produce dozens. At k = 1 (Poisson-like), transmission is more uniform. SARS, MERS, and SARS-CoV-2 all show k well below 1.
Anatomy of a Superspreading Event
Superspreading events share common features: enclosed spaces, poor ventilation, prolonged exposure, and activities that enhance aerosol production. Choir practices, meat-packing plants, cruise ships, and indoor religious services have all generated documented superspreading events. The physics is straightforward — an infectious person exhales pathogen-laden aerosols that accumulate in poorly ventilated spaces, exposing everyone present to high viral doses over extended periods.
Implications for Control
This simulation visualizes the negative binomial distribution of secondary cases. Adjust the dispersion parameter to see how the distribution shifts from uniform to highly skewed. The 80/20 fraction readout shows what proportion of cases drives most transmission. Watch the extinction probability change — with low k, most introductions die out, but the ones that do not can be explosive. This insight motivates targeted interventions: restrict superspreading conditions rather than all contact equally.