A carrier-borne epidemic with two stages of infection

This paper examines an epidemic spread by carriers, in which infectives may be in stage I or stage II of infection, depending on the number of contacts between the susceptibles, stage I infectives and carriers. A formal matrix solution for the state probabilities of the process is obtained, and the probabilities of survivors derived. A partial differential equation for the probability generating function of the process is also found, and its solution obtained in terms of Laplace transforms. Once again, the probabilities of survivors can be derived from these. The Laplace transforms may be inverted to provide time dependent solutions for the model.