The effects of vaccination to the dynamics of rubella virus with seasonality

Abstract

This paper studies the transmission model of rubella virus in the population of women of childbearing age who transmit the disease to babies they gave birth to. The analysis is divided for system with seasonality only and system with seasonality and vaccination. Basic reproduction number of the first system is calculated and used to determined the endemic state which corresponds to a stable periodic solution. The information, namely parameter values when endemic state of first system taken place are then used to study the impact of vaccination to control rubella transmission in the second system. The results shows that vaccination program is helpful to eradicate the virus. We also obtained the threshold for the coverage and efficacy of the vaccination program.