Discrete-time Markov chain approach to contact-based disease spreading in complex networks

2009/07/31 by Sergio Gómez, S. Gomez, Àlex Arenas +7 · 587 citations
Mathematics · Physics and Astronomy · #Algorithm #COVID-19 epidemiological studies #Complex Network Analysis Techniques #Computer science #Discrete time and continuous time #Focus (optics) #Machine learning #Markov chain #Markov process #Mathematics #Opinion Dynamics and Social Influence #Parameterized complexity #Physics #Statistics #Stochastic modelling #Stochastic process #Theoretical computer science #Vertex (graph theory) #physics.comp-ph #physics.soc-ph

paper · pdf · doi:10.1209/0295-5075/89/38009

published in Europhysics Letters (EPL) 89(3), 38009 (Institute of Physics) · 6 pages, 4 figures. Europhys Lett (in press 2010)

arxiv created 2010/01/23 · openalex publication_date 2010/02/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at a certain rate from an infected vertex to one neighbor at a time, and the reactive process (RP) in which an infected individual effectively contacts all its neighbors to expand the epidemics. However, a more realistic scenario is obtained from the interpolation between these two cases, considering a certain number of stochastic contacts per unit time. Here we propose a discrete-time formulation of the problem of contact-based epidemic spreading. We resolve a family of models, parameterized by the number of stochastic contact trials per unit time, that range from the CP to the RP. In contrast to the common heterogeneous mean-field approach, we focus on the probability of infection of individual nodes. Using this formulation, we can construct the whole phase diagram of the different infection models and determine their critical properties.

Citations

• Velocity and Hierarchical Spread of Epidemic Outbreaks in Scale-Free Networks
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