# Evolutionary dynamics of incubation periods

## TL;DR

This paper explains the common skewed distribution of incubation periods in diseases using evolutionary dynamics on networks, showing that stochastic processes can cause significant variability even in homogeneous populations.

## Contribution

It introduces a novel evolutionary graph model to explain incubation period variability, emphasizing stochastic mechanisms over heterogeneity.

## Key findings

- Skewed incubation periods emerge from stochastic processes like coupon collection and random walks.
- Results hold for homogeneous populations, not relying on heterogeneity.
- Model predicts individual variability in disease onset times despite equal exposure.

## Abstract

The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms. For typhoid fever, polio, measles, leukemia and many other diseases, 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. Although this statistical 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.