Most of us remember the frustration of trying to complete a collection of cards or stamps — you can never find the last one. In probability theory, this is known as the coupon collector's problem: owing to those long waits, the probability of completing a collection after a certain number of random draws is skewed to the right. Now it seems that the very same process may be at the origin of the incubation time for many diseases.
Take measles, polio or leukemia: extremely different diseases, and yet their incubation periods all follow an approximately log-normal distribution. Clinical experiments have ruled out the heterogeneity of conditions, such as patients' resilience, as the reason for this phenomenon.
Instead, Bertrand Ottino-Loffler and colleagues modelled the disease progression as that of a pathogen invading a network-structured population of cells. A right-skewed, approximately log-normal incubation time would naturally appear if symptoms were assumed to emerge just as a share of the network had been taken over. This explanation relies on the fundamental stochastic dynamics of the incubation process, afflicted by the same long waits experienced by the stamp collector.
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Levi, F. The discovery of skewness. Nat. Phys. 14, 108 (2018). https://doi.org/10.1038/nphys4354
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