Phase Diagram of the Contact Process on Barabasi-Albert Networks

TL;DR

This paper investigates the phase transition behavior of the contact process on Barabasi-Albert networks, revealing mean-field critical exponents, finite-size effects, and how the critical threshold varies with network connectivity.

Contribution

It provides a detailed analysis of the contact process on scale-free networks, including finite-size corrections and the relationship between network connectivity and epidemic thresholds.

Findings

Critical behavior follows mean-field exponents.

Finite-size logarithmic corrections vary among quasi-stationary states.

Critical threshold scales linearly with inverse connectivity, approaching the basic reproduction number R0=1 as connectivity increases.

Abstract

We show results for the contact process on Barabasi networks. The contact process is a model for an epidemic spreading without permanent immunity that has an absorbing state. For finite lattices, the absorbing state is the true stationary state, which leads to the need for simulation of quasi-stationary states, which we did in two ways: reactivation by inserting spontaneous infected individuals, or by the quasi-stationary method, where we store a list of active states to continue the simulation when the system visits the absorbing state. The system presents an absorbing phase transition where the critical behavior obeys the Mean Field exponents $\beta=1$, $\gamma'=0$, and $\nu=2$. However, the different quasi-stationary states present distinct finite-size logarithmic corrections. We also report the critical thresholds of the model as a linear function of the network connectivity inverse $1/z$, and the extrapolation of the critical threshold function for $z \to \infty$ yields the basic reproduction number $R_0=1$ of the complete graph, as expected. Decreasing the network connectivity leads to the increase of the critical basic reproduction number $R_0$ for this model.