Abstract |
While they are rare, superspreading events (SSEs), wherein a few primary cases infect an
extraordinarily large number of secondary cases, are recognized as a prominent determinant
of aggregate infection rates (R0). Existing stochastic SIR models incorporate SSEs by fitting
distributions with thin tails, or finite variance, and therefore predicting almost deterministic
epidemiological outcomes in large populations. This paper documents evidence from recent
coronavirus outbreaks, including SARS, MERS, and COVID-19, that SSEs follow a power
law distribution with fat tails, or infinite variance. We then extend an otherwise standard
SIR model with the fat-tailed power law distributions, and show that idiosyncratic uncertainties
in SSEs will lead to large aggregate uncertainties in infection dynamics, even with
large populations. That is, the timing and magnitude of outbreaks will be unpredictable.
While such uncertainties have social costs, we also find that they on average decrease the
herd immunity thresholds and the cumulative infections because per-period infection rates
have decreasing marginal effects. Our findings have implications for social distancing interventions:
targeting SSEs reduces not only the average rate of infection (R0) but also its
uncertainty. To understand this effect, and to improve inference of the average reproduction
numbers under fat tails, estimating the tail distribution of SSEs is vital.
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