Solvable epidemic model on degree-correlated networks

TL;DR

This paper introduces a simple method to incorporate degree correlation into epidemic models on networks, providing analytical formulas for outbreak thresholds and clarifying how degree correlation influences disease spread.

Contribution

It presents a novel analytical approach to account for degree correlation in epidemic models, which was previously considered difficult to analyze.

Findings

Degree correlation affects outbreak thresholds.

Analytical formulas for basic reproduction number are derived.

Degree correlation's impact on epidemic spread is clarified.

Abstract

Disease and information spread over social and information networks. Understanding the spread phenomena in networks requires paying attention not only to the degree distribution but also to the degree correlation. However, it is considered difficult to analytically deal with the effect of degree correlation on spread phenomena. Here, we introduce degree correlation using a simple method and present the theoretical formulas of the outbreak threshold and basic reproduction number. We theoretically clarify the effect of the degree correlation.