# Epidemic dynamics on random and scale-free networks

## DOI:

https://doi.org/10.21914/anziamj.v54i0.5770## Keywords:

degree distribution, Pareto distribution, power law, random graph, SIR model, superspreaders## Abstract

Random networks were first used to model epidemic dynamics in the 1950s, but in the last decade it has been realized that scale-free networks more accurately represent the network structure of many real-world situations. Here we give an analytical and a Monte Carlo method for approximating the basic reproduction number R0 of an infectious agent on a network. We investigate how final epidemic size depends on \(R_0\) and on network density in random networks and in scale-free networks with a Pareto exponent of three. Our results show that: (i) an epidemic on a random network has the same average final size as an epidemic in a well-mixed population with the same value of \(R_0\); (ii) an epidemic on a scale-free network has a larger average final size than in an equivalent well-mixed population if \(R_0\lt 1\), and a smaller average final size than in a well-mixed population if \(R_0\gt1\); (iii) an epidemic on a scale-free network spreads more rapidly than an epidemic on a random network or in a well-mixed population. doi:10.1017/S1446181112000302## Published

2013-01-30

## Issue

## Section

Special Issues on Mathematical Biology