Evolutionary dynamics of incubation periods

Abstract

The incubation period for typhoid, polio, measles, leukemia and many other diseases follows a right-skewed, approximately lognormal distribution. Although this pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here, we propose an explanation based on evolutionary dynamics on graphs. 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. Unlike previous explanations 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.

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

“…2), even though we used a single pathogen strain to infect a single host variety. This observation is consistent with recent modelling of distributions of incubation periods (Ottino-Loffler et al, 2017), but it contradicts the established view in the literature 430 on Z. tritici according to which lesions appear after an asymptomatic period of approximately two weeks (Kema et al, 1996;Steinberg, 2015). Shaw (1990) used pycnidiospores from the natural field population of Z. tritici to inoculate wheat plants in the greenhouse and found that lesions were appearing continuously during the period of up to 25-30 days.…”

Universal Statistics of Incubation Periods and Other Detection Times via Diffusion Models

“…Over the last hundred years, researchers accumulated a lot of data on incubation periods for various diseases in various populations. These data and the existing literature on the subject are thoroughly discussed in [BOL17], a recent paper that motivated the present study, so we are only giving a brief overview of the most imporant features of the data, referring to [BOL17] and references therein for further details.…”

“…All of these data show that within the same population group, a simultaneous exposure to the same pathogen does not result in simultaneous development of symptoms in all individuals belonging to the group. Instead, Figure 1: Data redrawn from historic examples (reproduced from [BOL17], with the authors' permission). Dashed red curves are lognormal densities and solid blue curves are Gumbel densities predicted in [BOL17].…”

“…Instead, Figure 1: Data redrawn from historic examples (reproduced from [BOL17], with the authors' permission). Dashed red curves are lognormal densities and solid blue curves are Gumbel densities predicted in [BOL17]. (a) Data from an outbreak of food-borne streptococcal sore throat, reported in [Sar50], time is measured in days.…”

“…The first explanations of the right-skewness were based on deterministic growth of the harmful agent population (such as exponential growth) with random parameters varying among individuals of the population and led to lognormal distribution of incubation times. However, there are cases discussed in [BOL17] where the randomness in these parameteres is lacking but right-skewed distributions resembling lognormal are still observed.…”