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Multi-body interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyse models for consensus dynamics on hypergraphs, where nodes interact in groups…
In this work, we aim to understand the influence of the heterogeneity of infection rates on the Susceptible-Infected-Susceptible (SIS) epidemic spreading. Employing the classic SIS model as the benchmark, we study the influence of the…
In previous work, we developed the scaled SIS process, which models the dynamics of SIS epidemics over networks. With the scaled SIS process, we can consider networks that are finite-sized and of arbitrary topology (i.e., we are not…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,…
We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
Graphs are a standard framework for describing dynamical processes shaped by pairwise interactions among agents. But many systems involve interactions in groups of three or more agents. Here, we develop a method of "$\ell$-hyperedge…
Various coarse-grained models have been proposed to study the spreading dynamics in the network. A microscopic theory is needed to connect the spreading dynamics with the individual behaviors. In this letter, we unify the description of…
We investigate the impact of network heterogeneity on synergistic contagion dynamics. By extending a synergistic contagion model to diverse heterogeneous network topologies, we uncover the emergence of novel dynamical regimes characterized…
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…
We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the…
To improve the accuracy of network-based SIS models we introduce and study a multilayer representation of a time-dependent network. In particular, we assume that individuals have their long-term (permanent) contacts that are always present,…
Most epidemic processes on networks can be modelled by a compartmental model, that specifies the spread of a disease in a population. The corresponding compartmental graph describes how the viral state of the nodes (individuals) changes…
Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions…
A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many…
We study a simple model of epidemics where an infected node transmits the infection to its neighbors independently with probability $p$. This is also known as the independent cascade or Susceptible-Infected-Recovered (SIR) model with fixed…
Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the…
Interactions in biology and social systems are not restricted to pairwise but can take arbitrary sizes. Extensive studies have revealed that the arbitrary-sized interactions significantly affect the spreading dynamics on networked systems.…
We introduce a spatial graph and hypergraph model that smoothly interpolates between a graph with purely pairwise edges and a graph where all connections are in large hyperedges. The key component is a spatial clustering resolution…