## Epidemic Models

*20 Oct 2019 11:15*

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.

(In fact, epidemic models on networks get their own notebook...)

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
- 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
- Valerie Isham and Graham Medley (eds.), Models for Infectious Human Diseases: Their Structure and Relation to Data
- Matt J. Keeling and Pejman Rohani, Modeling Infectious Diseases in Humans and Animals
- 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
- Maia Martcheva, An Introduction to Mathematical Epidemiology
- 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
- 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)