Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks

TL;DR

This paper introduces a simplified, compact pairwise model for multi-stage epidemic spread on complex networks, incorporating clustering and varying infectious periods, improving accuracy and reducing computational complexity.

Contribution

It develops a novel compact modeling approach that remains size-independent of node degree range and integrates clustering effects for more realistic epidemic predictions.

Findings

Model accurately captures multi-stage epidemic dynamics.

Clustering improves model realism and accuracy.

Constant infectious periods enhance closure performance.

Abstract

This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the complexity of the model. Network clustering is incorporated into the model to provide a more accurate representation of realistic contact networks, and the accuracy of proposed closures is analysed for different levels of clustering and number of infection stages. Our results support recent findings that standard closure techniques are likely to perform better when the infectious period is constant.