The spread of infectious disease through a population may be modeled as a stochastic process (typically a continuous-time Markov chain). For infections which are able to persist in the long term (i.e. become endemic in the population), a random variable of interest is the time until eventual extinction of infection.  Programmes exist aimed at global or regional eradication of specific diseases including polio, malaria, measles, onchocerciasis and others; economic planning for such programmes could potentially be helped by good estimates of the expected time to achieve disease extinction.  For relatively simple mathematical models, the expected persistence time may be computed exactly from general Markov process theory.  For more realistic models, this approach is no longer feasible, and approximations must be sought.  This project will use recently-developed methods from statistical mechanics to approximate persistence time for a variety of infectious transmission models, and investigate the effects of disease features (e.g. length of latent period, variability of infectious period, etc) upon this persistence time.