## Epidemic (Models) on Networks

*28 Sep 2020 10:32*

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

- Recommended (big picture):
- 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

- Recommended (historical):
- A. J. Lotka, Elements of Mathematical Biology, ch. VIII [It's become conventional to attribute epidemic models of this sort to Ross's work on malaria, and while that was certainly very important, Lotka's contemporary review of the literature, originally published in 1924, makes it clear that this was much more of a collective effort (as one might expect)]

- Recommended (close-ups):
- F. Altarelli, A. Braunstein, L. Dallâ€™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", arxiv:1810.03579
- 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.] - 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

- Recommended, close-ups on "vaccination" / removal of nodes or edges to limit propagation:
- 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

- "Resilience of the Internet to random breakdowns",
Physical Review Letters
- 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 - Q. Nguyen, H. D. Pham, D. Cassi and M.Bellingeri, "Conditional attack strategy for real-world complex networks", Physica A
**530**(2019): 121561 - 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] - 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] - Sebastian Wandelt, Xiaoqian Sun, Daozhong Feng, Massimiliano Zanin and Shlomo Havlin, "A comparative analysis of approaches to network-dismantling",
Scientific Reports
**8**(2018): 13513

- Noted without recommendation (and, unfairly, no explanation):
- Giannis Moutsinas, Choudhry Shuaib, Weisi Guo, Stephen Jarvis, "Graph hierarchy and spread of infections", arxiv:1908.04358

- Disrecommended:
- Some future time, when I'm feeling meaner.

- To read:
- 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 - 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 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
- J.-G. Caputo, A. Knippel, F. Mouatamide, M. Khaladi, "Analysis of an epidemic model on a network", arxiv:1906.07449
- Hocine Cherifi, Gergely Palla, Boleslaw K. Szymanski, Xiaoyan Lu, "On community structure in complex networks: challenges and opportunities", arxiv:1908.04901
- 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
- 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
- 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

- "Edge-based compartmental modeling for epidemic spread Part II: Model Selection and Hierarchies",
Journal of Mathematical Biology
- 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

- "Epidemic Spreading in Scale-Free Networks", Physical Review Letters
- 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 - 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 - 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