Evolutionary dynamics of incubation periods

ABSTRACT The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms 1 . For typhoid fever 2,3 , polio 4 , measles 5 , leukemia 6 and many other diseases 7–10 , the incubation period is highly variable. Some affected people take much longer than average to show symptoms, leading to a distribution of incubation periods that is right skewed and often approximately lognormal 8–10 . Although this statistical pattern was discovered more than sixty years ago 8 , it remains an open question to explain its ubiquity 11 . Here we propose an explanation based on evolutionary dynamics on graphs 12–18 . For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk 19,20 . Unlike previous explanations 11,21 that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease.