Extinction and outbreak probabilities
Stochastic epidemic models can assign probabilities to qualitatively different outcomes, such as early extinction or a substantial outbreak.
Early extinction
Even when a corresponding deterministic model predicts initial epidemic growth, a small number of infectious individuals can recover before producing enough new infections. The stochastic process can therefore reach the absorbing disease-free state.
Branching approximation
During the very early phase, when susceptible depletion is negligible, transmission can sometimes be approximated by a branching process. If each infectious individual independently produces offspring according to a distribution with probability-generating function \(G(s)\), the extinction probability \(q\) is the smallest solution in \([0,1]\) of
\[q=G(q).\]Simulation estimate
For more complicated models, extinction or outbreak probability can be estimated from repeated simulations by the fraction satisfying a clearly defined outcome criterion.