Vaccination against rubella: Analysis of the temporal evolution of the age-dependent force of infection and the effects of different contact patterns

Abstract

In this paper, we analyze the temporal evolution of the age-dependent force of infection and incidence of rubella, after the introduction of a very specific vaccination program in a previously nonvaccinated population where rubella was in endemic steady state. We deduce an integral equation for the age-dependent force of infection, which depends on a number of parameters that can be estimated from the force of infection in a steady state prior to the vaccination program. We present the results of our simulations, which are compared with observed data. We also examine the influence of contact patterns among members of a community on the age-dependent intensity of transmission of rubella and on the results of vaccination strategies. As an example of the theory proposed, we calculate the effects of vaccination strategies for four communities from Caieiras (Brazil), Huixquilucan (Mexico), Finland, and the United Kingdom. The results for each community differ considerably according to the distinct intensity and pattern of transmission in the absence of vaccination. We conclude that this simple vaccination program is not very efficient (very slow) in the goal of eradicating the disease. This gives support to a mixed strategy, proposed by Massad et al., accepted and implemented by the government of the State of São Paulo, Brazil.