Abstract

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 $$R_0$$, 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, $$R_0$$ overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to $$R_0$$ are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.