Measuring Infection Transmission in a Stochastic SIV Model with Infection Reintroduction and Imperfect Vaccine.

An additional compartment of vaccinated individuals is considered in a SIS stochastic epidemic model with infection reintroduction. The quantification of the spread of the disease is modeled by a continuous time Markov chain. A well-known measure of the initial transmission potential is the basic reproduction number [Formula: see text], which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Due to repeated contacts between the typical infective and previously infected individuals, [Formula: see text] overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to [Formula: see text] are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.