Controllability of Infections in SIR Models with Waned Childhood Vaccination-Induced Immunity and Booster Vaccination

Abstract

The aim of this paper is to study the controllability of infections represented by SIR endemic models with interventions based on vaccination and the impact of disease-induced reduction in contact-activity on the efforts required to eliminate the infection. Two kinds of vaccination-interventions are considered. The first is the routine-immunization, where a proportion p of newborns gets vaccinated immediately after birth and their immunity wanes overtime, while the other is to vaccinate those whose immunity acquired by routine-immunization waned and became susceptible again. The model analysis shows that the earlier the admission of booster vaccination is, the better the chance to eliminate the infection is. The analysis shows further that the higher the reduction in the contact activity of infected individuals is, the lower the booster vaccination rate needed to ensure an effective control of the infection is and, consequently, the less the minimum effort required to eliminate the infection is.