Epidemic dynamics on random and scale-free networks

James Bartlett, Michael John Plank

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

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v54i0.5770



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.