Epidemic threshold

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 the ratio between parameters $\lambda$ and $\mu$, which control the rate of spread and rate of recovery, respectively. For $\lambda /\mu$ above the epidemic threshold, epidemics take off and eventually become endemic. For $\lambda /\mu$ below the epidemic threshold, epidemics die out and eventually are completely absent from the population.

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