On the Duration of an Epidemic

A stochastic SIR (Susceptible, Infected, Recovered) model for the spread of a non-lethal disease is considered. The size of the population is constant. The problem of computing the moment-generating function of the random time until all members of the population are recovered is solved in special cases. The expected duration of the epidemic is also computed, as well as the probability that the whole population will be either cured or immunized before every member is infected. The method of similarity solutions is used to solve the various Kolmogorov partial differential equations, subject to the appropriate boundary conditions.