SIR Model of Epidemics: Herd Immunity

Excellent presentation at

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

Infection of susceptibles: dS/dt = - b S I

Infected: dI/dt = b S I - k I

Recovered/removed: dR/dt = k I

When the initial fraction of susceptibles, S0, is less than k/b = 1/(contact number),
the infection stops.