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In the mathematical modelling of infectious disease, the epidemic threshold quantifies the boundary between whether an epidemic will die out or will reach a sizable fraction of the population. Specifically, in compartmental models, it is a combination of rate parameters such that above a certain value, a small initial epidemic seed will on average increase in size with time.
For example, in the SIS epidemic model in a well-mixed population, the epidemic threshold is a condition on ratio between parameters and , which control the rate of spread and rate of recovery, respectively. For above the epidemic threshold, epidemics take off and eventually become endemic. For below the epidemic threshold, epidemics die out and eventually are completely absent from the population.
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