Optimal vaccination strategies—for whom?

Abstract

A SIRS model with vaccination is considered. The vaccination is assumed to have side effects (for simplicity, these side effects are modeled as a probability of becoming ill because of vaccination). It is the interest of the total population to minimize the prevalence of disease; hence, the vaccination rate that minimizes the prevalence will be determined. In Section 2, the individual is considered: an individual tries to minimize his or her own risk. This angle of approach results in a vaccination rate dependent on the prevalence of the disease. The bifurcations of this system are analyzed, and the optimal vaccination coverage for the individual is computed. This coverage is then compared with the optimal vaccination coverage for the total population: it is found that they disagree for some parameter sets.