Evolutionary Dynamics Of Incubation Periods
The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms1. For typhoid fever2,3, polio4, measles5, leukemia6 and many other diseases7-10, 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 lognormal8-10. Although this statistical pattern was discovered more than sixty years ago8, it remains an open question to explain its ubiquity11. Here we propose an explanation based on evolutionary dynamics on graphs12-18. 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 walk19,20. Unlike previous explanations11,21 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.