Spreading processes in Multilayer Networks (original) (raw)

Diffusion processes on multilayer networks

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social networks, or the diffusion of pathogens among individuals through their contact network, are fundamental phenomena occurring in these networks. However, while information diffusion in single networks has received considerable attention from various disciplines for over a decade, spreading processes in multilayer networks is still a young research area presenting many challenging research issues. In this paper we review the main models, results and applications of multilayer spreading processes and discuss some promising research directions.

The Effects of Diffusion of Information on Epidemic Spread --- A Multilayer Approach

Acta Physica Polonica B

In this work, the aim is to study the spread of a contagious disease and information on a multilayer social system. The main idea is to find a criterion under which the adoption of the spreading information blocks or suppresses the epidemic spread. A two-layer network is the base of the model. The first layer describes the direct contact interactions, while the second layer is the information propagation layer. Both layers consist of the same nodes. The society consists of five different categories of individuals: susceptibles, infective, recovered, vaccinated and precautioned. Initially, only one infected individual starts transmitting the infection. Direct contact interactions spread the infection to the susceptibles. The information spreads through the second layer. The SIR model is employed for the infection spread, while the Bass equation models the adoption of information. The control parameters of the competition between the spread of information and spread of disease are the topology and the density of connectivity. The topology of the information layer is a scale-free network with increasing density of edges. In the contact layer, regular and scale-free networks with the same average degree per node are used interchangeably. The observation is that increasing complexity of the contact network reduces the role of individual awareness. If the contact layer consists of networks with limited range connections, or the edges sparser than the information network, spread of information plays a significant role in controlling the epidemics.

Epidemics spreading in interconnected complex networks

Physics Letters A, 2012

We study epidemic spreading in two interconnected complex networks. It is found that in our model the epidemic threshold is always lower than that in any of the two standalone networks. Detailed theoretical analysis is proposed which allows quick and accurate calculations of epidemic threshold and average outbreak/epidemic size. Theoretical analysis and simulation results show that, generally speaking, the epidemic size is not significantly affected by the inter-network correlation. In interdependent networks which can be viewed as a special case of interconnected networks, however, impacts of inter-network correlation on the epidemic threshold and outbreak size are more significant.

Modeling the Spread of Multiple Contagions on Multilayer Networks

A susceptible-infected-susceptible (SIS) model of multiple contagions on multilayer networks is developed to incorporate different spreading channels and disease mutations. The basic reproduction number for this model is estimated analytically. In a special case when considering only compartmental models, we analytically analyze an example of a model with a mutation driven strain persistence characterized by the absence of an epidemic threshold. This model is not related to the network topology and can be observed in both compartmental models and models on networks. The novel multiplecontagion SIS model on a multilayer network could help in the understanding of other spreading phenomena including communicable diseases, cultural characteristics, addictions, or information spread through e-mail messages, web blogs, and computer networks.

Dynamical interplay between awareness and epidemic spreading in multiplex networks

We present the analysis of the interrelation between two processes accounting for the spreading of an epidemics, and the information awareness to prevent its infection, on top of multiplex networks. This scenario is representative of an epidemic process spreading on a network of persistent real contacts, and a cyclic information awareness process diffusing in the network of virtual social contacts between the same individuals. The topology corresponds to a multiplex network where two diffusive processes are interacting affecting each other. The analysis using a Microscopic Markov Chain Approach (MMCA) reveals the phase diagram of the incidence of the epidemics and allows to capture the evolution of the epidemic threshold depending on the topological structure of the multiplex and the interrelation with the awareness process. Interestingly, the critical point for the onset of the epidemics has a critical value (meta-critical point) defined by the awareness dynamics and the topology of the virtual network, from which the onset increases and the epidemics incidence decreases. PACS numbers: 89.65.-s, 89.75.Fb, 89.75.Hc

The Diffusion of Viral Content in Multi-layered Social Networks

Modelling the diffusion of information is one of the key areas related to activity within social networks. In this field, there is recent research associated with the use of community detection algorithms and the analysis of how the structure of communities is affecting the spread of information. The purpose of this article is to examine the mecha-nisms of diffusion of viral content with particular emphasis on cross community diffusion.

Competing spreading processes on multiplex networks: awareness and epidemics

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Epidemiclike spreading processes on top of multilayered interconnected complex networks reveal a rich phase diagram of intertwined competition effects. A recent study by the authors [C. Granell et al., Phys. Rev. Lett. 111, 128701 (2013).] presented an analysis of the interrelation between two processes accounting for the spreading of an epidemic, and the spreading of information awareness to prevent infection, on top of multiplex networks. The results in the case in which awareness implies total immunization to the disease revealed the existence of a metacritical point at which the critical onset of the epidemics starts, depending on completion of the awareness process. Here we present a full analysis of these critical properties in the more general scenario where the awareness spreading does not imply total immunization, and where infection does not imply immediate awareness of it. We find the critical relation between the two competing processes for a wide spectrum of parameters ...

Epidemic spread in human networks

IEEE Conference on Decision and Control and European Control Conference, 2011

One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the Susceptible-Infected-Susceptible (SIS) model has been widely used. In the SIS model, each node can be susceptible, become infected with a given infection rate, and become again susceptible with a given curing rate. In this paper, we add a new compartment to the classic SIS model to account for human response to epidemic spread. Each individual can be infected, susceptible, or alert. Susceptible individuals can become alert with an alerting rate if infected individuals exist in their neighborhood. An individual in the alert state is less probable to become infected than an individual in the susceptible state; due to a newly adopted cautious behavior. The problem is formulated as a continuous-time Markov process on a general static graph and then modeled into a set of ordinary differential equations using mean field approximation method and the corresponding Kolmogorov forward equations. The model is then studied using results from algebraic graph theory and center manifold theorem. We analytically show that our model exhibits two distinct thresholds in the dynamics of epidemic spread. Below the first threshold, infection dies out exponentially. Beyond the second threshold, infection persists in the steady state. Between the two thresholds, the infection spreads at the first stage but then dies out asymptotically as the result of increased alertness in the network. Finally, simulations are provided to support our findings. Our results suggest that alertness can be considered as a strategy of controlling the epidemics which propose multiple potential areas of applications, from infectious diseases mitigations to malware impact reduction.

HETEROGENEOUS EPIDEMIOLOGIC INFLUENCE SPREADING MODELS IN COMPLEX NETWORKS

2009

Many of the systems around us are connected in networks with complex patterns forming a complex networks. The individuals of these networks interact among each other tending to impose theirs own state to the surrounding individuals. Such tendencies cause dynamic processes in complex networks defined as influence spreading. There is a big diversity of such processes, and their research gives important results for predicting the speed and rate of spreading of many processes like natural viruses, computer viruses, social processes etc.