This talk considers extinction times for birth-death Markov processes with an absorbing state, whose rates depend on a control parameter that defines a threshold and on a population scale N, with the deterministic continuum limit reached as N goes to infinity. The Susceptible-Infected-Susceptible (SIS) model serves as the typical example. An exact expression for the mean extinction time is presented, along with its leading-order asymptotics for large N: logarithmic in N below the threshold, proportional to the square root of N at the threshold, and exponential in N (divided by the square root of N) above it. The Fokker-Planck approximation, obtained by replacing the difference equation with a differential one, is shown to be correct only in some special cases. The talk is based on work submitted to the SIAM MMS Special Issue on Multiscale Modeling in Biology.