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][9][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][13][14][15][16][17][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.The discovery that incubation periods tend to follow right-skewed distributions originally came from epidemiological investigations of incidents in which many people were simultaneously and inadvertently exposed to a pathogen. For example, at a church dinner in Hanford, California on March 17, 1914, ninety-three individuals became infected with typhoid fever after eating contaminated spaghetti prepared by an asymptomatic carrier known to posterity as Mrs. X. Using the known time of exposure and onset of symptoms for the 93 cases, Sawyer 2 found that the incubation periods ranged from 3 to 29 days, with a mode of only 6 days and a distribution that was strongly skewed to the right. Similar results were later found for other infectious diseases. Surveying the literature in 1950, Sartwell noted a striking pattern: the incubation periods of diseases as diverse as streptococcal sore throat 8 (Fig. 1a), measles 22 (Fig. 1b), polio, malaria, chicken pox, and the common cold were all, to a good approximation, lognormally distributed 8 .

Self-regulation of phenotypic noise synchronizes emergent organization and active transport in confluent microbial environments

“…3a,e, 4 and 5), in agreement with previous reports 34,35 . The log-normal nature of the ℓ b and AR, which we confirm theoretically (equation (10a)), is observed frequently in natural systems and stems from the underlying independent random variables [34][35][36][37] . This confirms that the distribution of AR is ultimately determined by that of ℓ b , provided the variability in growth rate remains low, as reported previously 38 .…”

The reachability of contagion in temporal contact networks: how disease latency can exploit the rhythm of human behavior

“…Epidemics occur when the latent period is close to 20 and 42 h. We note that large epidemics are likely across a larger range of latent period modes in the second cluster due to the larger variance in the distribution of latent periods. This is a consequence of the fact that incubation (and thus latent) periods follow a log-Normal distribution for which higher mean results in a higher variance [ 46 ].…”

Measurement of infection efficiency of a major wheat pathogen using time‐resolved imaging of disease progress

“…On the contrary, they appeared continuously during a period of up to 3 weeks, even though a single pathogen strain was used to infect a single host variety. This observation is consistent with recent modelling of distributions of incubation periods (Ottino‐Loffler et al ., ), but it contradicts the established view in the literature on Z. tritici , according to which lesions appear after a symptomless period of approximately 2 weeks (Kema et al ., ; Steinberg, ). Shaw () used pycnidiospores from the natural field population of Z. tritici to inoculate wheat plants in the greenhouse and found that lesions appeared continuously during a period of up to 25–30 days; however, the asynchronicity in lesion appearance could have resulted from the variation in latent period between different pathogen strains as well as the ‘developmental’ asynchronicity within a single pathogen genotype that was observed in the present study.…”