# Epidemic threshold

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

## References

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