Compartmental models are a basic tool in epidemiology.

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Compartmental models are a basic tool in epidemiology. SIR ( susceptible-infected-recovered) models are among the simplest compartmental models. They model potential transitions of a set of individuals or homogenous regions between states of susceptibility (S), infection (I), and recovery (R). In an SIR model, a susceptible individual may become an infected individual through contact with another infected individual. An infected individual may recover. Recovered individuals gain immunity and are therefore not susceptible to reinfection. An infected person might instead die, in which case they are also not susceptible (and so death is technically a subcategory of recovery).

SIR models can be conveniently modeled by a main loop in which a simulated clock or calendar moves forward in regular increments. These regular increments, or "ticks" of the virtual clock, provide an approximation of continuous time in which many individuals may be evolving concurrently. To maintain an illusion that all individuals evolve simultaneously, each simulation cycle (tick) is divided into two parts. In the first part, a next state for each individual is computed, using only the current states of other individuals. (Thus the order in which we loop through individuals does not matter.) In the second part, each individual advances to its next state (and again the order in which we loop through individuals doesn't matter).

 

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