After vaccination, vaccinees acquire some protection against infection and/or disease. Vaccination, therefore, reduces the number of infections in the population. Due to this herd immunity, not everybody needs to be vaccinated to prevent infections from spreading.
Eichner, et al. (2017) quantify direct and indirect effects of influenza vaccination examining the standard Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) model as well as simulation results of a sophisticated simulation tool which allows for seasonal transmission of four influenza strains in a population with realistic demography and age-dependent contact patterns.
As shown analytically for the simple SIR and SIRS transmission models, indirect vaccination effects are bigger than direct ones if the effective reproduction number of disease transmission is close to the critical value of 1. Simulation results for 20 percent to 60 percent vaccination with live influenza vaccine of 2-17 year-old children in Germany, averaged over 10 years (2017–26), confirm this result: four to seven times as many influenza cases are prevented among non-vaccinated individuals as among vaccinees. For complications like death due to influenza which occur much more frequently in the unvaccinated elderly than in the vaccination target group of children, indirect benefits can surpass direct ones by a factor of 20 or even more than 30.
The researchers conclude that true effect of vaccination can be much bigger than what would be expected by only looking at vaccination coverage and vaccine efficacy.
Reference: Eichner M, et al. Direct and indirect effects of influenza vaccination. BMC Infectious Diseases. 2017;17:308