相关论文: Exact and approximate epidemic models on networks:…

The ongoing need for effective epidemic modeling has driven advancements in capturing the complex dynamics of infectious diseases. Traditional models, such as Susceptible-Infected-Recovered, and graph-based approaches often fail to account…

Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the time scales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios,…

Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…

Exact solutions of the SEIR epidemic model are derived, and various properties of solutions are obtained directly from the exact solution. In this paper Abel differential equations play an important role in establishing the exact solution…

Modeling spreading processes in complex random networks plays an essential role in understanding and prediction of many real phenomena like epidemics or rumor spreading. The dynamics of such systems may be represented algorithmically by…

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 consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model…

The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…

We explore a rigorous formulation of agent-based SIR epidemic dynamics as a discrete-state Markov process, capturing the stochastic propagation of infection or an invading agent on networks. Using indicator functions and corresponding…

We investigate the time-evolution and steady states of the stochastic susceptible-infected-recovered-susceptible(SIRS) epidemic model on one- and two- dimensional lattices. We compare the behavior of this system, obtained from computer…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

In this paper, we study the spread of a classical SIR process on a two-layer random network, where the first layer represents the households, while the second layer models the contacts outside the households by a random scale-free graph. We…

The importance of modeling the spread of epidemics through a population has led to the development of mathematical models for infectious disease propagation. A number of empirical studies have collected and analyzed data on contacts between…

We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…

Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…

In this paper, we develop a node-based approximate model for Markovian contagion dynamics on networks. We prove that our approximate model is exact for SIR (susceptible-infectious-recovered) and SEIR…

Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that enlarge a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the…

We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…

We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be…

Finding large "cliquish" subgraphs is a central topic in graph mining and community detection. A popular clique relaxation are 2-clubs: instead of asking for subgraphs of diameter one (these are cliques), one asks for subgraphs of diameter…