Epidemics (or Epidemic Models) on Networks

Last update: 06 Feb 2026 14:19
First version: 9 November 2019 (or earlier)

Yet Another Inadequate Placeholder, at the intersection of epidemic models and network data analysis.

Branching Processes

Alun L. Lloyd and Robert M. May, "How Viruses Spread Among Computers and People", Science 292 (2001): 1316--1317
Istaván Z. Kiss, Joel C. Miller and Peter L. Simon, Mathematics of Epidemics on Networks: From Exact to Approximate Models [Review]
Mark E. J. Newman, "The spread of epidemic disease on networks", Physical Review E 66 (2002): 016128, arxiv:cond-mat/0205009

F. Altarelli, A. Braunstein, L. Dall'Asta, and R. Zecchina, "Large deviations of cascade processes on graphs", Physical Review E 87 (2013): 062115, arxiv:1305.5745 [See comments under "Social Contagion, Information Cascades, Diffusion of Innovations, Etc."]
Frank Ball, Denis Millison and Gianpaolo Scalia-Tomba, "Epidemics with Two Levels of Mixing", Annals of Applied Probability 7 (1997): 46--89
Tom Britton, "Epidemic models on social networks -- with inference", arxiv:1908.05517
Moez Draief and Laurent Massoulié, Epidemics and Rumors in Complex Networks
Dean Eckles, Elchanan Mossel, M. Amin Rahimian, Subhabrata Sen, "Long ties accelerate noisy threshold-based contagions", Nature Human Behavior 8 (2024): 1057--1064, arxiv:1810.03579
Y. Moreno, R. Pastor-Satorras and A. Vespignani
- "Epidemic Spreading in Scale-Free Networks", Physical Review Letters 86 (2001): 3200
- "Epidemic dynamics and endemic states in complex networks", Physical Review E 63 (2001): 066117
- "Epidemic outbreaks in complex heterogeneous networks", European Physical Journal B 26 (2002): 521--529
Hao Peng, Azadeh Nematzadeh, Daniel M. Romero, Emilio Ferrara, "Network Modularity Controls the Speed of Information Diffusion", arxiv:1910.05870
Thomas House, Matt J Keeling, "Epidemic prediction and control in clustered populations", Journal of Theoretical Biology 272 (2011): 1--7, arxiv:1012.1974
Eben Kenah and James M. Robins, "Second look at the spread of epidemics on networks", Physical Review E 76 (2007): 036113, arxiv:q-bio.QM/0610057
Seth A. Marvel, Travis Martin, Charles R. Doering, David Lusseau and M. E. J. Newman, "The small-world effect is a modern phenomenon", arxiv:1310.2636
R. M. May and R. M. Anderson, "The Transmission Dynamics of Human Immunodeficiency Virus (HIV)", Philosophical Transactions of the Royal Society of London B 321 (1988): 565--607 [This remarkable paper is the oldest one I can find which works out the consequences for an SIR model of randomly-varying but uncorrelated node degrees (section 4.1). Thus for instance they show that this makes the epidemic threshold \( \propto \frac{\mathrm{mean\ degree}}{\mathrm{mean\ squared\ degree}} \). There's a chunk of work in the physics literature from the early 2000s which is just re-discovering this. (More remarkably, May was of course trained as a theoretical physicist.) JSTOR.]
Joel C. Miller, Anja C. Slim, Erik M. Volz, "Edge-Based Compartmental Modeling for Infectious Disease Spread Part I: An Overview", Journal of the Royal Society: Interface 9 (2012): 890--906, arxiv:1106.6320
Joel C. Miller, Erik M. Volz
- "Edge-based compartmental modeling for epidemic spread Part II: Model Selection and Hierarchies", Journal of Mathematical Biology 67 (2013): 869--899, arxiv:1106.6319
- "Edge-Based Compartmental Modeling for Infectious Disease Spread Part III: Disease and Population Structure", PLoS ONE 8 (2013): e69162, arxiv:1106.6344
Xiao-Long Peng, Xin-Jian Xu, Xinchu Fu, and Tao Zhou, "Vaccination intervention on epidemic dynamics in networks", Physical Review E 87 (2013): 022813, arxiv:1302.5979 ["Vaccination" here means random movement from a high-susceptibility state (the ordinary S) into a low-susceptibility state, and random movement back.]
Guillaume St-Onge, Vincent Thibeault, Antoine Allard, Louis J. Dubé, Laurent Hébert-Dufresne, "School closures, event cancellations, and the mesoscopic localization of epidemics in networks with higher-order structure", arxiv:2003.05924 [Assume the network is bipartite, with one part being individuals and the other "sites", events or places, and that individuals can share the disease through, but only through, contact at the sites. Further assume a heavy-tailed distribution for degree on both sides. Then the prevalence at the high-degree sites can be much higher than the over-all prevalence, and the removing the high-degree sites can drastically raise the epidemic threshold.]
Lisa Sattenspiel (with Alun Lloyd), The Geographic Spread of Infectious Diseases: Models and Applications [Covers network models as one approach to geography, among others. JSTOR]
Laura M. Smith, Kristina Lerman, Cristina Garcia-Cardona, Allon G. Percus and Rumi Ghosh, "Spectral Clustering with Epidemic Diffusion", Physical Review E 88 (2013): 042813, arxiv:1303.2663
Didia Vega-Oliveros, Luciano da F Costa and Francisco A. Rodrigues, "Rumor propagation with heterogeneous transmission in social networks", Journal of Statistical Mechanics: Theory and Experiment (2017): 023401, arxiv:1610.01012

Reuven Cohen, Keren Erez, Daniel ben-Avraham, Shlomo Havlin
- "Resilience of the Internet to random breakdowns", Physical Review Letters 85 (2000): 4626--4628, arxiv:cond-mat/0007048
- "Breakdown of the Internet under intentional attack", Physical Review Letters 86 (2001): 3682--3685, arxiv:cond-mat/0010251
Zhen Dai, Ping Li, Yan Chen, Kai Zhang, Jie Zhang, "Influential node ranking via randomized spanning trees", Physica A 526 (2019): 120625 [This is a purely numerical paper, but I find their centrality measure charmingly simple, and strongly suspect it's a Monte Carlo estimate of something more classical]
Víctor M. Eguíluz and Konstantin Klemm, "Epidemic Threshold in Structured Scale-Free Networks", Physical Review Letters 89 (2002): 108701, arxiv:cond-mat/0205439 [But graphs generated by this model are very weird, and that's really what drives the results --- see Moreno and Vazquez (2003) below]
Petter Holme, Beom Jun Kim, Chang No Yoon, and Seung Kee Han, "Attack vulnerability of complex networks", Physical Review E 65 (2002): 056109, arxiv:cond-mat/0202410
N. Madar, T. Kalisky, R. Cohen, D. ben-Avraham, S. Havlin, "Immunization and epidemic dynamics in complex networks", European Physical Journal B 38 (2004): 269--276 [Not on arxiv? --- Interestingly, their "acquaintance" immunization strategy, which essentially uses the friendship paradox to preferentially immunize the high-degree nodes without having to know who they are, is the idea I "came up with" for the still-unpublished project code-named "Do not adjust your receiver". Since that idea came to me sometime around 2013, it's entirely possible I was guided by subconscious memories of this paper (hence my scare-quotes around "came up with"). I should finish that project.]
Yamir Moreno, Alexei Vazquez, "Disease Spreading in Structured Scale-Free Networks", European Physical Journal B 31 (2003): 265--271, arxiv:cond-mat/0210362 [On Eguíluz and Klemm]
Q. Nguyen, H. D. Pham, D. Cassi and M.Bellingeri, "Conditional attack strategy for real-world complex networks", Physica A 530 (2019): 121561
Romualdo Pastor-Satorras and Alessandro Vespignani, "Immunization of complex networks", Physical Review E 65 (2002): 036104, arxiv:cond-mat/0107066
Christian M. Schneider, Tamara Mihaljev, Shlomo Havlin, and Hans J. Herrmann, "Suppressing epidemics with a limited amount of immunization units" Physical Review E 84 (2011): 061911, arxiv:1102.1929 [Their method is to target the nodes (or edges) whose vaccination will result in the largest decrease in the number of susceptible nodes in the resulting connected component. I believe them that this lowers the probability of infection, compared to the Holme et al. strategy of targeting nodes with high betweenness, but the differences are frankly very small for their real-world networks]
Michael Taylor, Timothy J. Taylor, Istvan Z. Kiss, "Epidemic threshold and control in a dynamic network", Physical Review E 85 (2012): 016103, arxiv:1110.4000
Sebastian Wandelt, Xiaoqian Sun, Daozhong Feng, Massimiliano Zanin and Shlomo Havlin, "A comparative analysis of approaches to network-dismantling", Scientific Reports 8 (2018): 13513

Giannis Moutsinas, Choudhry Shuaib, Weisi Guo, Stephen Jarvis, "Graph hierarchy and spread of infections", arxiv:1908.04358

Some future time, when I'm feeling meaner.

Antoine Allard, Pierre-André Noël, Louis J. Dubé, Babak Pourbohloul, "Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics", Physical Review E 79 (2009): 036113, arxiv:0811.2349
Andrea J. Allen, Mariah C. Boudreau, Nicholas J. Roberts, Antoine Allard, Laurent Hébert-Dufresne, "Predicting the diversity of early epidemic spread on networks", Physical Review Research 4 (2022): 013123, arxiv:2107.03334
Nino Antulov-Fantulin, Alen Lancic, Hrvoje Stefancic, Mile Sikic, Tomislav Smuc, "Statistical inference framework for source detection of contagion processes on arbitrary network structures", arxiv:1304.0018
Frank Ball, Tom Britton, David Sirl, "A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon", arxiv:1207.3205 Probability 44 (2012): 63--86
Frank Ball and David Sirl, "An SIR epidemic model on a population with random network and household structure, and several types of individuals", Advances in Applied Probability 44 (2012): 63--86
Romulus Breban, Raffaele Vardavas and Sally Blower, "Linking population-level models with growing networks: A class of epidemic models", Physical Review E 72 (2005): 046110
Fan Bu, Allison E. Aiello, Jason Xu, Alexander Volfovsky, "Likelihood-based Inference for Partially Observed Epidemics on Dynamic Networks", arxiv:1910.04221
Guido Caldarelli, Oriol Artime, Giulia Fischetti, Stefano Guarino, Andrzej Nowak, Fabio Saracco, Petter Holme, Manlio de Domenico, "The Physics of News, Rumors, and Opinions", arxiv:2510.15053
J.-G. Caputo, A. Knippel, F. Mouatamide, M. Khaladi, "Analysis of an epidemic model on a network", arxiv:1906.07449
Kihong Chung, Yongjoo Baek, Daniel Kim, Meesoon Ha, Hawoong Jeong, "Generalized epidemic process on modular networks", arxiv:1312.0573
Emilie Coupechoux, Marc Lelarge, "Contagions in Random Networks with Overlapping Communities", arxiv:1303.4325
Leon Danon, Ashley P. Ford, Thomas House, Chris P. Jewell, Matt J. Keeling, Gareth O. Roberts, Joshua V. Ross, Matthew C. Vernon, "Networks and the Epidemiology of Infectious Disease", arxiv:1011.5950
Dolev Dilmoney, Bnaya Gross, Shlomo Havlin, Nadav M. Shnerb, "Dynamics of critical cascades in interdependent networks", arxiv:2504.06862
Irene A. Doherty, Nancy S. Padian, Cameron Marlow, Sevgi O. Aral, "Determinants and Consequences of Sexual Networks as They Affect the Spread of Sexually Transmitted Infections", The Journal of Infectious Diseases 191 (2005): S42--S54
Xinchu Fu, Michael Small, Guanrong Chen, Propagation Dynamics on Complex Networks: Models, Methods and Stability Analysis
Benjamin Golub and Matthew O. Jackson, "Using selection bias to explain the observed structure of Internet diffusions", Proceedings of the National Academy of Sciences (USA) 107 (2010): 10833--10836
Sergio Gomez, Jesus Gomez-Gardenes, Yamir Moreno, Alex Arenas, "Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks", Physical Review E 84 (2011): 036105, arxiv:1106.6184
Alison L. Hill, David G. Rand, Martin A. Nowak, Nicholas A. Christakis, "Infectious Disease Modeling of Social Contagion in Networks", PLOS Computational Biology 6 (2010): e1000968
Jason Hindes, Sarabjeet Singh, Christopher R. Myers, David J. Schneider, "Epidemic fronts in complex networks with metapopulation structure", arxiv:1304.4310
Petter Holme, "Model versions and fast algorithms for network epidemiology", arxiv:1403.1011
Thomas House, "Modelling Epidemics on Networks", arxiv:1111.4875
Brian Karrer and M. E. J. Newman, "Message passing approach for general epidemic models", Physical Review E 82 (2010): 016101, arxiv:1003.5673
Marcelo N. Kuperman, "Invited review: Epidemics on social networks", arxiv:1312.3838
Hsuan-Wei Lee, Nishant Malik, Feng Shi, and Peter J. Mucha, "Social clustering in epidemic spread on coevolving networks", Physical Review E 99 (2019): 062301
Kristina Lerman, Xiaoran Yan, Xin-Zeng Wu, "The Majority Illusion in Social Networks", PLOS One 11 (2016): e0147617, arxiv:1506.03022
Longzhao Liu, Xin Wang, Yi Zheng, Wenyi Fang, Shaoting Tang, Zhiming Zheng, "Homophily on social networks changes evolutionary advantage in competitive information diffusion", arxiv:1908.05992
Su-Yu Liu, Andrea Baronchelli, and Nicola Perra, "Contagion dynamics in time-varying metapopulation networks", Physical Review E 87 (2013): 032805
Naoki Masuda, Konstantin Klemm, Víctor M. Eguíluz, "Temporal networks: slowing down diffusion by long lasting interactions", arxiv:1305.2938
Alexander M. Mercier, Samuel V. Scarpino, Cristopher Moore, "Effective Resistance for Pandemics: Mobility Network Sparsification for High-Fidelity Epidemic Simulation", arxiv:2111.02449
Sifat Afroj Moon, Faryad Darabi Sahneh, Caterina Scoglio, "Generalized group-based epidemic model for spreading processes on networks: GgroupEM", arxiv:1908.06057
Géza Ódor, "Spectral analysis and slow spreading dynamics on complex networks", arxiv:1306.3401
Romualdo Pastor-Satorras and Alessandro Vespignani
- "Epidemic Spreading in Scale-Free Networks", Physical Review Letters 86 (2001): 3200--3203
- "Epidemic dynamics and endemic states in complex networks", Physical Review E 63 (2001): 066117
Joshua L. Payne, Kameron Decker Harris, and Peter Sheridan Dodds, "Exact solutions for social and biological contagion models on mixed directed and undirected, degree-correlated random networks", Physical Review E 84 (2011): 016110
Ignacio A. Perez, Paul A. Trunfio, Cristian E. La Rocca, Lidia A. Braunstein, "Controlling distant contacts to reduce disease spreading on disordered complex networks", Physica A 545 (2020): 123709, arxiv:1908.06147
Prapanporn Rattana, Konstantin B. Blyuss, Ken T. D. Eames, Istvan Z. Kiss, "A Class of Pairwise Models for Epidemic Dynamics on Weighted Networks", Bulletin of Mathematical Biology 75 (2013): 466--490, arxiv:1208.6036
Martin Ritchie, Luc Berthouze, Istvan Z. Kiss, "Beyond clustering: Mean-field dynamics on networks with arbitrary subgraph composition", Journal of Mathematical Biology 72 (2016): 255--281, arxiv:1405.6234
Tim Rogers, "Maximum-entropy moment-closure for stochastic systems on networks", Journal of Statistical Mechanics (2011): P05007, arxiv:1103.4980
Zhongyuan Ruan, Gerardo Iniguez, Marton Karsai, Janos Kertesz, "Kinetics of Social Contagion", Physical Review Letters 115 (2015): 218702
Faryad Darabi Sahneh, Caterina Scoglio, Fahmida N. Chowdhury, "Effect of Coupling on the Epidemic Threshold in Interconnected Complex Networks: A Spectral Analysis", arxiv:1212.4194
M. Ángeles Serrano and Marián Boguñá, "Percolation and Epidemic Thresholds in Clustered Networks", Physical Review Letters 97 (2006): 088701
Mile Sikic, Alen Lancic, Nino Antulov-Fantulin, Hrvoje Stefancic, "Epidemic centrality and the underestimated epidemic impact on network peripheral nodes", arxiv:1110.2558
Daniel Smilkov, Ljupco Kocarev, "The influence of the network topology on epidemic spreading", arxiv:1111.3176
Daniel Smilkov, Cesar A. Hidalgo, Ljupco Kocarev, "Beyond network structure: How heterogenous susceptibility modulates the spread of epidemics", arxiv:1403.2708
Michele Starnini, Anna Machens, Ciro Cattuto, Alain Barrat, Romualdo Pastor-Satorras, "Immunization strategies for epidemic processes in time-varying contact networks", arxiv:1305.2357
Clara Stegehuis, Remco van der Hofstad & Johan S. H. van Leeuwaarden , "Epidemic spreading on complex networks with community structures", Scientific Reports 6 (2016): 29748
Francesco Vincenzo Surano, Christian Bongiorno, Lorenzo Zino, Maurizio Porfiri, and Alessandro Rizzo, "Backbone reconstruction in temporal networks from epidemic data", Physical Review E 100 (2019): 042306
Ali Tavasoli, Teague Henry, Heman Shakeri, "A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic model", arxiv:2108.02005
L. D. Valdez, L. A. Braunstein, S. Havlin, "Epidemic spreading on modular networks: the fear to declare a pandemic", arxiv:1909.09695
Erik M. Volz, Joel C. Miller, Alison Galvani and Lauren Ancel Meyers, "Effects of Heterogeneous and Clustered Contact Patterns on Infectious Disease Dynamics", PLoS Computational Biology 7 (2011): e1002042
Huijuan Wang, Qian Li, Gregorio D'Agostino, Shlomo Havlin, H. Eugene Stanley, Piet Van Mieghem, "Effect of the Interconnected Network Structure on the Epidemic Threshold", arxiv:1303.0781
Wei Wang,, Ming Tang, H. Eugene Stanley and Lidia A. Braunstein, "Unification of theoretical approaches for epidemic spreading on complex networks", Reports on Progress in Physics 80 (2017): 036603
Stefan Wieland, Tomas Aquino, Ana Nunes, "The structure of coevolving infection networks", Europhysics Letters 97 (2012): 18003, arxiv:1111.7267
Damian H. Zanette, Sebastian Risau Gusman, "Infection spreading in a population with evolving contacts", arxiv:0711.0874
Johannes Zierenberg, Jens Wilting, Viola Priesemann, Anna Levina, "Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence", Physical Review E 101 (2020): 022301, arxiv:1905.10402