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

TL;DR

This paper reviews epidemic models like SIS and contact process on complex networks, focusing on phase transitions to disease-free states and how network properties influence epidemic thresholds and critical behavior.

Contribution

It provides a concise overview of well-known epidemic models on complex networks, emphasizing phase transitions and the impact of network heterogeneity.

Findings

SIS model's epidemic threshold depends on network heterogeneity.

Critical exponents relate to network statistical properties.

Models predict the transition between disease-free and endemic states.

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.