Epidemic Models

05 Mar 2024 11:46

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 being exposed and becoming infectious (SEIR); 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