More succintly: In the SIR (Susceptible, Infected, Resolved) epidimic model, r0 is the ratio of dI/dt / dR/dt. r0 < 1 means people are recovering at a rate fa

More succintly: In the SIR (Susceptible, Infected, Resolved) epidimic model, r0 is the ratio of dI/dt / dR/dt. r0 < 1 means people are recovering at a rate faster than new people are getting sick. If each new case, on average results in less than one new case, and all cases eventually resolve (recovery or death), then it's a mathematical truth that the number of active cases must go down over time. The decrease isn't necessarily monotonic, but over a long enough time frame it's inevitable. The bursty nature of super-spreading will produce variance, but as long as these super-spreaders are accounted for in the observed r0, the variance itself doesn't change the long-term outcome. Now, the estimated/measured r0 is just a sample/estimate of the (unknowable) "true" r0, and r0 isn't constant, but those are separate issues.