Measuring infection transmission in a stochastic SIV model with infection reintroduction and imperfect vaccine

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, 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 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 are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.