An overview of epidemic models with phase transitions to absorbing states running on top of complex networks

Abstract

Dynamical systems running on the top of complex networks has been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact process (CP) and the susceptible-infected-susceptible (SIS) model are used quite often to describe epidemic dynamics. Despite their simplicity, these models are robust to predict the kernel of real situations. In this work, we review concisely both processes that are well-known and very applied examples of models that exhibit absorbing-state phase transitions. In the epidemic scenario, individuals can be infected or susceptible. A phase transition between a disease-free (absorbing) state and an active stationary phase (where a fraction of the population is infected) are separated by an epidemic threshold. For the SIS model, the central issue is to determine this epidemic threshold on heterogeneous networks. For the CP model, the main interest is to relate critical exponents with statistical properties of the network.

References in corpus (15)

• Critical phenomena in complex networks
• Thresholds for epidemic spreading in networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Griffiths phases on complex networks
• Finite-size scaling in complex networks
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks
• Predicting the speed of epidemics spreading on networks
• Routes to thermodynamic limit on scale-free networks
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Quasi-stationary analysis of the contact process on annealed scale-free networks
• Reply to the Comment on the paper "Non-mean-field behavior of the contact process on scale-free networks"
• Localization transition, Lifschitz tails and rare-region effects in network models
• The lifespan method as a tool to study criticality in absorbing-state phase transitions
• Equivalence of conditional and external field ensembles in absorbing state phase transitions

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