Study of Extinction Time

In this thesis we study an epidemic spreading through a finite population where each individual can be susceptible (S), infective (I), and return to being susceptible (S), and we track the number of individuals in each state as time progresses. In contrast to the deterministic case which is modeled by systems of ODEs, we consider infection and recovery to be stochastic (random) events. Interest is in the (random) time T at which the epidemic dies out. For a large number of initial infectives, the time for extinction is governed by the ratio of the infection and recovery rates. For a small number of initial infectives, the epidemic may die out quickly due to random effects even if the infection and recovery rates would predict otherwise