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The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.<\/jats:p>","DOI":"10.1155\/2017\/4253167","type":"journal-article","created":{"date-parts":[[2017,8,28]],"date-time":"2017-08-28T17:01:18Z","timestamp":1503939678000},"page":"1-11","source":"Crossref","is-referenced-by-count":1,"title":["Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics"],"prefix":"10.1155","volume":"2017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9799-0183","authenticated-orcid":true,"given":"Lee","family":"Worden","sequence":"first","affiliation":[{"name":"Francis I. 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