The spread of epidemic disease on networks

Abstract

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.

12 pages, 3 figures

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• Community structure in social and biological networks

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• Information spreading on dynamic social networks
• EMH: Extended Mixing H-index centrality for identification important users in social networks based on neighborhood diversity
• A Random Walk Perspective on Hide-and-Seek Games
• Sample NLPDE and NLODE Social-Media Modeling of Information Transmission for Infectious Diseases:Case Study Ebola
• Degree and component size distributions in generalized uniform recursive tree
• A survey of results on mobile phone datasets analysis
• Quickest Inference of Network Cascades with Noisy Information
• On Strategic Defense of Stochastic Networks
• Invited review: Epidemics on social networks
• The end time of SIS epidemics driven by random walks on edge-transitive graphs
• Dynamic Vaccination Game in a Heterogeneous Mixing Population
• Epidemic modelling requires knowledge of the social network
• Epidemics in a Synthetic Urban Population with Multiple Levels of Mixing
• Error Propagation Through a Network With Non-Uniform Failure
• Data-Driven Allocation of Vaccines for Controlling Epidemic Outbreaks
• On "Sexual contacts and epidemic thresholds," models and inference for Sexual partnership distributions
• Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements
• Conditions for viral influence spreading through multiplex correlated social networks
• Solution of the Voter Model by Spectral Analysis
• Degree dependent transmission rates in epidemic processes
• Degree-ordered percolation on hierarchical scale-free network
• Double transitions and hysteresis in heterogeneous contagion processes
• Structural Analysis of Viral Spreading Processes in Social and Communication Networks Using Egonets
• SIR epidemics in dynamic contact networks
• Degree product rule tempers explosive percolation in the absence of global information
• Individual based SIS models on (not so) dense large random networks
• SIR epidemics on evolving graphs
• Distribution of outbreak sizes for SIR disease in finite populations
• Comparing the diversity of information by word-of-mouth vs. web spread
• Percolation on a maximally disassortative network
• Temporal Dynamics of Connectivity and Epidemic Properties of Growing Networks
• Hubs-biased resistance distances on graphs and networks
• Approaching the thermodynamic limit in equilibrated scale-free networks
• Effect of time-dependent infectiousness on epidemic dynamics
• Percolation of the Site Random-Cluster Model by Monte Carlo Method
• A sampling-guided unsupervised learning method to capture percolation in complex networks
• Scale-free random branching tree in supercritical phase
• Peak fraction of infected in epidemic spreading for multi-community networks
• Models for digitally contact-traced epidemics
• Deterministic Random Walk Model in NetLogo and the Identification of Asymmetric Saturation Time in Random Graph
• Thermally activated intermittent flow in amorphous solids
• Scaling and universality for percolation in random networks: A unified view
• Rational Neural Networks for Approximating Jump Discontinuities of Graph Convolution Operator
• Time Evolution of Non-Lethal Infectious Diseases: A Semi-Continuous Approach
• Mitigating Biological Epidemic on Heterogeneous Social Networks
• Diffusion of Real-Time Information in Social-Physical Networks
• Contact Tracing: Computational Bounds, Limitations and Implications
• Detecting and modelling real percolation and phase transitions of information on social media
• Population-scale testing can suppress the spread of infectious disease
• Modeling the spread of infectious disease in urban areas with travel contagion
• Systemic Risk: Fire-Walling Financial Systems Using Network-Based Approaches
• Stochastic epidemic-type model with enhanced connectivity: exact solution
• New Insights from an Analysis of Social Influence Networks under the Linear Threshold Model
• Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics
• Cumulative Merging Percolation: A long-range percolation process in networks
• A new method for the robust characterisation of pairwise statistical dependency between point processes
• Dynamical Properties of Interaction Data
• Modeling Internet-Scale Policies for Cleaning up Malware
• Locally self-organized quasi-critical percolation in a multiple disease model
• Backtracking activation impacts the criticality of excitable networks
• A weighted planar stochastic lattice with scale-free, small-world and multifractal properties
• Tight Bounds for Connectivity of Random K-out Graphs
• A re-entrant phase transition in the survival of secondary infections on networks
• Effectiveness of Rapid Rail Transit System in Beijing
• A Graph-Neural-Network-Entropy model of vital node identification on network attack and propagation
• Video Pandemics: Worldwide Viral Spreading of Psy's Gangnam Style Video
• Heterogeneity in Outcomes of Repeated Instances of Percolation Experiments
• Strength and weakness of disease-induced herd immunity in networks
• Disease Transmission on Random Graphs Using Edge-Based Percolation
• No-exclaves percolation on random networks
• The network epidemiology of an Ebola epidemic
• Early Indicators of COVID-19 Spread Risk Using Digital Trace Data of Population Activities
• Scaling in the global spreading patterns of pandemic Influenza A (H1N1) and the role of control: empirical statistics and modeling
• Diffusion in Colocation Contact Networks: the Impact of Nodal Spatiotemporal Dynamics
• Epidemic dynamics on complex networks
• Synchronizability and synchronization dynamics of weighed and unweighed scale free networks with degree mixing
• Digital Epidemiology: A review
• Dynamic communicability and epidemic spread: a case study on an empirical dynamic contact network
• Exact analytical solution of irreversible binary dynamics on networks
• Asymmetrically interacting spreading dynamics on complex layered networks
• A note on a paper by Erik Volz [arXiv:0705.2092]: SIR dynamics in random networks
• Monotonic and Non-Monotonic Epidemiological Models on Networks
• Numerical assessment of the percolation threshold using complement networks
• Exact rank-reduction of network models
• On the Effectiveness of Tracking and Testing in SEIR Models
• Law of large numbers for the SIR epidemic on a random graph with given degrees
• Parameter estimation for contact tracing in graph-based models
• Iterative Site Percolation on Triangular Lattice
• Complex Contagions and hybrid phase transitions in unclustered and clustered random networks
• Upper Bounds on Overshoot in SIR Models with Nonlinear Incidence
• The Co-evolution of Cooperation and Epidemic Spreading
• Temporal and probabilistic comparisons of epidemic interventions
• D-chain tomography of networks: a new structure spectrum and an application to the SIR process
• Indirect Influence on Network Diffusion
• Localization of nonbacktracking centrality on dense subgraphs of sparse networks
• Diffusion in Networks With Overlapping Community Structure
• Comparison of theoretical approaches for epidemic processes with waning immunity in complex networks
• An exact N-strain epidemic model using bond percolation
• Recommendation systems in the scope of opinion formation: a model
• Limits of Multilayer Diffusion Network Inference in Social Media Research
• Stochasticity of infectious outbreaks and consequences for optimal interventions
• Identifying influential subpopulations in metapopulation epidemic models using message-passing theory
• Multivariate Generating Functions for Information Spread on Multi-Type Random Graphs
• Dynamic Exploration of Networks: from general principles to the traceroute process
• Expected Extinction Times of Epidemics with State-Dependent Infectiousness
• Optimal Curing Strategy for Competing Epidemics Spreading over Complex Networks
• Diffusion Based Network Embedding
• Pandemic Spread in Communities via Random Graphs
• Deep Generative Modeling in Network Science with Applications to Public Policy Research
• Combinatorial approach to spreading processes on networks
• Optimal Control of Interdependent Epidemics in Complex Networks
• SIR dynamics in random networks with heterogeneous connectivity
• A survey on modelling of infectious disease spread and control on social contact networks
• Estimation of Small s-t Reliabilities in Acyclic Networks
• Semi-Supervised Record Linkage for Construction of Large-Scale Sociocentric Networks in Resource-limited Settings: An application to the SEARCH Study in Rural Uganda and Kenya
• A node-based SIRS epidemic model with infective media on complex networks
• Benchmarking Measures of Network Influence
• Double Transition in a Model of Oscillating Percolation
• Cost Effective Campaigning in Social Networks
• Leveraging Evolution Dynamics to Generate Benchmark Complex Networks with Community Structures
• Collective Influence of Multiple Spreaders Evaluated by Tracing Real Information Flow in Large-Scale Social Networks
• Inferring $R_0$ in emerging epidemics - the effect of common population structure is small
• Phase transition for parameter learning of Hidden Markov Models
• Limiting the Neighborhood: De-Small-World Network for Outbreak Prevention
• Contact Graph Epidemic Modelling of COVID-19 for Transmission and Intervention Strategies
• Real-time Updating of Dynamic Social Networks for COVID-19 Vaccination Strategies
• Near-critical SIR epidemic on a random graph with given degrees
• Vaccination with partial transmission and social distancing on contact networks
• Mechanisms of recoverable prevalence and extinction of viruses on linearly growing scale-free networks
• Detecting a trend change in cross-border epidemic transmission
• Epidemic-like Proximity-based Traffic Offloading
• Connected components in networks with higher-order interactions
• Epidemics on evolving networks with varying degrees
• Network structure and disease risk for an endemic infectious disease
• A rigorous and efficient approach to finding and quantifying symmetries in complex networks
• PRRS Outbreak Prediction via Deep Switching Auto-Regressive Factorization Modeling
• Analysis of the Impact of Mask-wearing in Viral Spread: Implications for COVID-19
• Growing a Network on a Given Substrate
• Exact epidemic models from a tensor product formulation
• Maximizing spreading in complex networks with risk in node activation
• Fair treatment allocations in social networks
• Awareness and Movement vs. the Spread of Epidemics - Analyzing a Dynamic Model for Urban Social/Technological Networks
• Interaction between cluster synchronization and epidemic spread in community networks
• Modified SI Epidemic Model for Combating Virus Spread in Spatially Correlated Wireless Sensor Networks
• Game among Interdependent Networks: The Impact of Rationality on System Robustness
• Finding an individual's probability of infection in an SIR network is NP-hard
• Quantifying Uncertainty in Stochastic Models with Parametric Variability
• Tight Bounds for Influence in Diffusion Networks and Application to Bond Percolation and Epidemiology
• Degree-layer theory of network topology
• Continuum Cascade Model of Directed Random Graphs: Traveling Wave Analysis
• A Comparative Analysis of Influenza Vaccination Programs
• Spatio-Temporal Graphical Model Selection
• Percolation in clustered networks
• Continuum Percolation on Disoriented Surfaces: the Problem of Permeable Disks on a Klein Bottle
• Diffusion on dynamic contact networks with indirect transmission links
• Generalized Erdos Numbers for network analysis
• Rumors in a Network: Who's the Culprit?
• Directionality reduces the impact of epidemics in multilayer networks
• A cavity approach to optimization and inverse dynamical problems
• SoReC: A Social-Relation Based Centrality Measure in Mobile Social Networks
• Discrimination universally determines reconstruction of multiplex networks
• Robustness of Information Diffusion Algorithms to Locally Bounded Adversaries
• In Response to COVID-19: Configuration Model of the Epidemic Spreading
• Real-time growth rate for general stochastic SIR epidemics on unclustered networks
• On the Accuracy of Deterministic Models for Viral Spread on Networks
• Derivation and Characteristics of Closed-Form Solutions of the Fundamental Equations for Online User Dynamics
• Efficient message passing for cascade size distributions on finite trees
• A novel method based on node correlation to evaluate the important nodes in complex networks
• Mapping structural diversity in networks sharing a given degree distribution and global clustering: Adaptive resolution grid search evolution with Diophantine equation-based mutations
• Permutation Tests for Infection Graphs
• Assessing Individual and Community Vulnerability to Fake News in Social Networks
• Closed-Form Solutions of the Fundamental Equation That Describes User Dynamics in Online Social Networks
• Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States
• Impact of behavioral heterogeneity on epidemic outcome and its mapping into effective network topologies
• Modeling and Analysis of Cascading Failures in Interdependent Cyber-Physical Systems
• Effects of Noise on Ecological Invasion Processes: Bacteriophage-mediated Competition in Bacteria
• Multi-Stage Complex Contagions in Random Multiplex Networks
• Household Bubbling Strategies for Epidemic Control and Social Connectivity
• Superstable Geometry in Triadic Percolation
• Tracking dynamics of superspreading through contacts, exposures, and transmissions in edge-based network epidemics
• The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable
• Exact mean field dynamics for epidemic-like processes on heterogeneous networks
• A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon
• Epidemics on networks with large initial conditions or changing structure
• Simulation-Optimization Approaches for the Network Immunization Problem with Quarantining
• Predicting epidemics on weighted networks
• Manageable to unmanageable transition in a fractal model of project networks
• On the Analysis of a Label Propagation Algorithm for Community Detection
• Continuous Models of Epidemic Spreading in Heterogeneous Dynamically Changing Random Networks
• Dynamical patterns of epidemic outbreaks in complex heterogeneous networks
• A heuristic optimization method for mitigating the impact of a virus attack
• Percolation on the institute-enterprise R&D collaboration networks
• Bilinear effect in complex systems
• Large Deviation Principle for the Exploration Process of the Configuration Model
• Epidemic spreading with immunization on bipartite networks
• Does social distancing matter for infectious disease propagation? A SEIR model and Gompertz law based cellular automaton
• Link Cascades in Complex Networks: A Mean-field Approach
• Parameter Estimation in Epidemic Spread Networks Using Limited Measurements
• Perturbative expansion of the fundamental equation of online user dynamics for describing changes in eigenfrequencies
• Information Theoretic Adaptive Tracking of Epidemics in Complex Networks
• Percolation Thresholds of Updated Posteriors for Tracking Causal Markov Processes in Complex Networks
• The duration of an $SIR$ epidemic on a configuration model
• Epidemics with asymptomatic transmission: Sub-critical phase from recursive contact tracing
• Ranking the spreading influence of nodes in complex networks based on mixing degree centrality and local structure
• The human monogamy behavior can influence the transmission of AIDS
• Consequence of doping in spatiotemporal rock-paper-scissors games
• Generalized individual-based epidemic model for vulnerability assessment of correlated scale-free complex networks
• Epidemic and Cascading Survivability of Complex Networks
• Recovery of Interdependent Networks
• Epidemic spread in networks: Existing methods and current challenges
• Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure
• Two Categories of Indoor Interactive Dynamics of a Large-scale Human Population in a WiFi covered university campus
• Epidemics and vaccination on weighted graphs
• An epidemic in a dynamic population with importation of infectives