Evolutionary dynamics of incubation periods

Area of Science:

• Mathematical biology
• Epidemiology
• Network science

Background:

• Many diseases, including typhoid, polio, and measles, exhibit incubation periods that follow a right-skewed, lognormal distribution.
• The underlying reasons for the ubiquity of this distribution across diverse diseases remain largely unexplained despite being observed over 60 years ago.

Purpose of the Study:

• To propose and investigate an explanation for the widespread occurrence of skewed incubation period distributions.
• To explore the role of evolutionary dynamics on structured populations in generating these distributions.

Main Methods:

• Modeling the invasion of a network-structured population by a mutant or pathogen.
• Analyzing simple models incorporating varying invader fitness, competition dynamics, and network structures.
• Applying concepts from probability theory, specifically the coupon collector and random walk problems.

Main Results:

• Skewed incubation period distributions emerge naturally from the proposed models across a broad range of parameters.
• The observed skewness can be explained by stochastic mechanisms inherent in the models, not solely by population heterogeneity.
• Results hold true even for homogeneous populations, challenging previous explanations.

Conclusions:

• Evolutionary dynamics on network-structured populations provide a robust explanation for the common lognormal, right-skewed distribution of disease incubation periods.
• Stochastic processes, rather than population heterogeneity, are identified as key drivers of this distributional pattern.
• The findings predict significant variability in disease onset even under identical exposure conditions due to inherent randomness.