A monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling

TL;DR

This paper proves that in pairwise epidemic models, lower variance in infectious periods results in higher outbreak sizes, highlighting a monotonic relationship between infectious period variability and epidemic magnitude.

Contribution

The study establishes a theoretical link between infectious period variance and epidemic size in non-Markovian models, supported by stochastic simulations.

Findings

Lower infectious period variance increases the basic reproduction number.

Smaller variance leads to larger epidemic outbreaks.

Results are consistent across different network structures.

Abstract

For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number, and consequently to a larger epidemic outbreak, when the mean infectious period is fixed. We discuss how this result is related to various stochastic orderings of the distributions of infectious periods. The results are illustrated by a number of explicit stochastic simulations, suggesting that their validity goes beyond regular networks.