Basic reproduction number \(R_0\)
The basic reproduction number \(R_0\) is the expected number of secondary infections produced by a typical infectious individual introduced into a fully susceptible population, under the assumptions of the model.
Simple SIR model
For the basic frequency-dependent SIR model,
\[R_0=\frac{\beta}{\gamma}.\]The threshold interpretation is
\[R_0>1:\ \text{initial growth is possible},\qquad R_0<1:\ \text{infection declines near the disease-free state}.\]Model dependence
The formula for \(R_0\) changes when the model contains additional infectious stages, age structure, vectors, heterogeneous mixing or other mechanisms.
Key idea. \(R_0\) is a model-derived invasion threshold, not a universal biological constant.