Infection dynamics on scale-free networks

2001/11/19 by Robert M. May, Alun L. Lloyd · 17 citations
Physics and Astronomy · Psychology · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Mental Health Research Topics

paper · doi:10.1103/physreve.64.066112

openalex publication_date 2001/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

We discuss properties of infection processes on scale-free networks, relating them to the node-connectivity distribution that characterizes the network. Considering the epidemiologically important case of a disease that confers permanent immunity upon recovery, we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual's degree of connectivity within the population. As in an earlier study [R. Pastor-Satorras and A. Vesipignani, Phys. Rev. Lett. 86, 3200 (2001); Phys. Rev. E. 63, 006117 (2001)] for an infection that did not confer immunity upon recovery, the epidemic process--in contrast with many traditional epidemiological models--does not exhibit threshold behavior, and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale-free network. Finally, we discuss effects that arise from finite population sizes, showing that networks of finite size do exhibit threshold effects: infections cannot spread for arbitrarily low transmission probabilities.

Citations

• Emergence of scaling in random networks
• Error and attack tolerance of complex networks
• On power-law relationships of the Internet topology

Cited by

• Mixing patterns in networks
• INTERPLAY BETWEEN HIV/AIDS EPIDEMICS AND DEMOGRAPHIC STRUCTURES BASED ON SEXUAL CONTACT NETWORKS
• Model hierarchies in edge-based compartmental modeling for infectious disease spread
• Assessing interaction networks with applications to catastrophe dynamics and disaster management
• The spread of disease with birth and death on networks
• The spread of infectious disease on complex networks with household-structure
• Nonlinear Spread of Rumor and Inoculation Strategies in the Nodes With Degree Dependent Tie Strength in Complex Networks
• Epidemic Dynamics on an Adaptive Network
• Epidemic spreading on heterogeneous networks with identical infectivity
• Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics
• Transitivity reinforcement in the coevolving voter model
• Zealotry effects on opinion dynamics in the adaptive voter model
• Inhomogeneous percolation models for spreading phenomena in random graphs
• Tuning degree distributions: Departing from scale-free networks
• Rate equation approach for correlations in growing network models
• Emergence of Persistent Infection due to Heterogeneity
• Compartmental models (epidemiology) [wikipedia]