Impact of the infectious period on epidemics

TL;DR

This paper investigates how the variability in the infectious period affects epidemic spread across various models, demonstrating that increased variability generally reduces epidemic severity and reachability.

Contribution

It establishes a monotonic relationship between infectious period variability and epidemic probability across multiple models, including non-Markovian and network-based frameworks.

Findings

Epidemic severity decreases as infectious period variance increases.

Variability in infectious period dampens epidemic spread even when R0 is fixed.

Delay and ordinary differential equations can bound infection probabilities.

Abstract

The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise, message passing, and spatial models as special cases. For this model, we prove a monotonic relationship between the variability of the infectious period (with fixed mean) and the probability that the infection will reach any given subset of the population by any given time. For certain families of distributions, this result implies that epidemic severity is decreasing with respect to the variance of the infectious period. The striking importance of this relationship is demonstrated numerically. We then prove, with a fixed basic reproductive ratio (R0), a monotonic relationship between the variability of the posterior transmission probability (which is a function of the infectious period) and the probability that the infection will reach any given subset of the population by any given time. Thus again, even when R0 is fixed, variability of the infectious period tends to dampen the epidemic. Numerical results illustrate this but indicate the relationship is weaker. We then show how our results apply to message passing, pairwise, and Kermack-McKendrick epidemic models, even when they are not exactly consistent with the stochastic dynamics. For Poisson contact processes, and arbitrarily distributed infectious periods, we demonstrate how systems of delay differential equations and ordinary differential equations can provide upper and lower bounds, respectively, for the probability that any given individual has been infected by any given time