## Epidemic Models

*31 May 2018 16:07*

These are a specialized class of stochastic process, originally inspired by epidemiology, but widely applied in the social sciences, e.g., to model the spread of information through social contagion ("going viral", as we say). The most basic form divides the members of the population into two classes, the "susceptible" and the "infected"; contact between a susceptible person and an infected one can, with some probability, make the susceptible person infected. This is called an "SI" model. A natural refinement is to make the period of infectiousness finite, with a distinction between a formerly infectious person becoming susceptible again ("SIS"), or recovered or otherwise removed from the population ("SIR"); a delayed period between becoming infected and becoming infectious; whether the probability of transmission depends on the total number of infected individuals or depends on details of geography and social networks; etc., etc.

See also: Agent-based Modeling; Complex Networks; Dynamics; Ecology; Evolution; Interacting Particle Systems; Memes and the "epidemiology of beliefs"; Statistics

- Recommended:
- M. S. Bartlett
- Stochastic Population Models in Ecology and Epidemiology
- "The Relevance of Stochastic Models for Large-Scale Epidemiological Phenomena", Journal of the Royal Statistical Society C
**13**(1964): 2--8

- Nino Boccara, Modeling Complex Systems [ Review]
- Stephen P. Ellner and John Guckenheimer, Dynamic Models in Biology

- To read:
- 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
- Lamia Belhadji, "Ergodicity and hydrodynamic limits for an epidemic model", arxiv:0710.5185
- 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 - 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
- D. J. Daley and J. Gani, Epidemic Modeling: An Introduction
- 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
- Odo Diekmann, Hans Heesterbeek and Tom Britton, Mathematical Tools for Understanding Infectious Disease Dynamics
- Romain Guy, Catherine Larédo, Elisabeta Vergu, "Approximation of epidemic models by diffusion processes and their statistical inference", arxiv:1305.3492
- 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
- Valerie Isham and Graham Medley (eds.), Models for Infectious Human Diseases: Their Structure and Relation to Data
- Istvan Z. Kiss, Joel C. Miller and Peter L. Simon, Mathematics of Epidemics on Networks: From Exact to Approximate Models
- Amanda A. Koepke, Ira M. Longini, Jr., M. Elizabeth Halloran, Jon Wakefield, Vladimir N. Minin, "Predictive Modeling of Cholera Outbreaks in Bangladesh", arxiv:1402.0536
- Marcelo N. Kuperman, "Invited review: Epidemics on social networks", arxiv:1312.3838
- Su-Yu Liu, Andrea Baronchelli, and Nicola Perra, "Contagion dynamics in time-varying metapopulation networks", Physical Review E
**87**(2013): 032805 - Maia Martcheva, An Introduction to Mathematical Epidemiology
- 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", arxiv:1106.6320
- Joel C. Miller, Erik M. Volz, "Edge-based compartmental modeling for epidemic spread Part II: Model Selection and Hierarchies", arxiv:1106.6319
- Géza Ódor, "Spectral analysis and slow spreading dynamics on complex networks", arxiv:1306.3401
- 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 - Xiao-Long Peng, Xin-Jian Xu, Xinchu Fu, and Tao Zhou, "Vaccination intervention on epidemic dynamics in networks", Physical Review E
**87**(2013): 022813 - 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
- 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
- Steffen Unkel, C. Paddy Farrington, Paul H. Garthwaite, Chris Robertson, Nick Andrews, "Statistical methods for the prospective detection of infectious disease outbreaks: a review", Journal of the Royal Statistical Society A forthcoming (2011)
- 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
- Damian H. Zanette, Sebastian Risau Gusman, "Infection spreading in a population with evolving contacts", arxiv:0711.0874