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

TL;DR

This paper introduces a discrete-time Markov chain model for contact-based epidemic spreading in complex networks, bridging the gap between contact process and reactive process by considering stochastic contact trials.

Contribution

It develops a unified discrete-time framework that interpolates between existing epidemic models, focusing on individual node infection probabilities.

Findings

Constructed the phase diagram for various contact models

Determined critical properties of the epidemic spreading

Bridged the gap between contact process and reactive process

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.