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Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…
In this paper, we focus on the node-based epidemic modeling for networks, introduce the propagation medium and propose a node-based Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infective media. Theoretical…
The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known \textit{Susceptible-Infected-Susceptible} ($SIS$) epidemic…
In spite of the study of epidemic dynamics on single-layer networks has received considerable attention, the epidemic dynamics on multiplex networks is still limited and is facing many challenges. In this work, we consider the…
This paper studies epidemic processes over discrete-time periodic time-varying networks. We focus on the susceptible-infected-susceptible (SIS) model that accounts for a (possibly) mutating virus. We say that an agent is in the disease-free…
Recently, research that focuses on the rigorous understanding of the relation between simulation and/or exact models on graphs and approximate counterparts has gained lots of momentum. This includes revisiting the performance of classic…
In this paper we study the household-structure SIS epidemic spreading on general complex networks. The household structure gives us the way to distinguish inner and the outer infection rate. Unlike household-structure models on homogenous…
Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
This paper investigates the spread of infectious diseases within a networked community by integrating epidemic transmission and public opinion dynamics. We propose a novel discrete-time networked SIS (Susceptible-Infectious-Susceptible)…
Although we have made progress in understanding disease spread in complex systems with non-Poissonian activity patterns, current models still fail to capture the full range of recovery time distributions. In this paper, we propose an…
We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where…
We study structural changes of adaptive networks in the co-evolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the…
It has been shown in the past that many real-world networks exhibit community structures and non-trivial clustering which comes with the occurrence of a notable number of triangular connections. Yet the influence of such connection patterns…
Epidemic propagation on complex networks has been widely investigated, mostly with invariant parameters. However, the process of epidemic propagation is not always constant. Epidemics can be affected by various perturbations, and may bounce…
This work is concerned with epidemiological models defined on networks, which highlight the prominent role of the social contact network of a given population in the spread of infectious diseases. In particular, we address the modelling and…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
Analyzing and controlling spreading processes are challenging problems due to the involved non-linear node (subsystem) dynamics, unknown disturbances, complex interconnections, and the large-scale and multi-level nature of the problems. The…
We study convergence properties of competing epidemic models of the Susceptible-Infected-Susceptible (SIS) type. The SIS epidemic model has seen widespread popularity in modelling the spreading dynamics of contagions such as viruses,…
An accurate approximate formula of the die-out probability in a SIS epidemic process on a network is proposed. The formula contains only three essential parameters: the largest eigenvalue of the adjacency matrix of the network, the…