18.104.22.168. Dynamics in the longer term
An important difference between the SIR and SIS (or SIRS) model is that the susceptible population is not replenished. In the SIR model, the progress of the epidemic continually reduces the susceptible population. Eventually, this depletion reduces the rate at which new infections can arise: SIR epidemics are self-limited and the infection eventually goes extinct.
This self-limitation typically occurs as the number of susceptibles passes below some threshold value: consequently, some fraction of the population will typically escape infection. In such settings, the severity of the epidemic is measured by the so-called size of the epidemic: the fraction (or number) of individuals who ever experience infection over the entire course of the outbreak.
In the SIS and SIRS settings, replenishment of the susceptible population means that it is possible for the infection to become permanently established in the population. In the simplest settings, the typical outcome is that the system approaches an equilibrium—the endemic equilibrium— at which there is a positive prevalence of infection. Endemic infections are possible in the SIR framework if demography is accounted for, since births provide another means by which the susceptible pool can be replenished.
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