An Algorithmic Study of S-I-R Stochastic Epidemic Models

Algorithms for the S-I-R epidemic with an initial population with m infectives and n susceptibles are examined. We propose efficient algorithms for the distributions of the total and the maximum size of the epidemic, and for the joint distribution of the maximum and the time of its occurrence. We also discuss the joint distribution of the sizes of the epidemic at two epochs. By studying the Markov chain describing an indefinite replication of the epidemic, we obtain new descriptors of the process of infections.