Direct and indirect effects of influenza vaccination

Abstract

Background: 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 protection, not everybody needs to be vaccinated to prevent infections from spreading.

Methods: We 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.

Results: 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 20-60% 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.

Conclusions: The true effect of vaccination can be much bigger than what would be expected by only looking at vaccination coverage and vaccine efficacy.

Fig. 1

a-b SIR model describing the transmission of infection in a population (S: susceptible, I: infectious, R: immune, V vaccinated). a Standard SIR model where a fraction v is vaccinated at birth and immediately becomes immune. b Modified SIR model with vaccinees who can become infected. Parameters: per capita birth and death rate μ, contact rate β, recovery rate γ, population size N. The full model description is given in the Additional file 1

Fig. 2

Ratio of indirect/direct vaccination effects in the SIR model. This ratio does not depend on the vaccination coverage as long as it does not completely prevent the spread of infection

Fig. 3

a-b SIRS model describing the transmission of infection in a population (S: susceptible, I: infectious, R: immune, V vaccinated). a Standard SIRS model with protective vaccination. b Modified SIRS model with vaccinees who can become infected. Parameters: per capita birth and death rate μ, contact rate β, recovery rate γ, vaccination rate ϕ, loss rate of naturally acquired immunity ρ, loss rate of vaccination-derived immunity τ, population size N. The full model description is given in the Additional file 1

Fig. 4

Ratio of indirect/direct vaccination effects in the SIRS model for different vaccination rates (from top to bottom: ϕ = 0.2, 0.1, 0.01 per year). As the whole population is eligible for vaccination in the SIRS model, transmission can go to extinction for moderately high annual vaccination coverage if R₀ is small (thus, the lines cannot be drawn for the whole R₀ range). Parameters: life expectancy μ⁻¹ = 70 years, duration of naturally acquired immunity ρ ⁻¹ = 6 years, duration of vaccination-derived immunity τ⁻¹ = 2 years, duration of contagiousness γ⁻¹ = 5 days. The mathematical description of the curves is given in the Additional file 1

Fig. 5

a-c Simulation results of pediatric QLAIV vaccination in Germany. Each bar represents the results for 10 years (2017–26): dark grey: indirectly prevented cases among adults, light grey: indirectly prevented cases among children, white: directly prevented cases among children, black: remaining cases which are not prevented. Numbers above the bars give the ratios “all indirectly prevented cases” / “all directly prevented cases”. Simulations are initialized from 2000 to 2016 using TIV with the baseline vaccination coverage. In the 10-year period starting with 2017, vaccinations are switched to QIV (reference scenario) and the effect of additional QLAIV vaccination of 2–17 years old children is evaluated. In the QLAIV scenario, children below 2 and adults receive QIV as in the reference scenario; in the first evaluation year the QLAIV coverage of 2–17 year old children is identical to the baseline coverage (around 5%), then it is increased stepwise for 3 years to reach a final coverage of 20 to 60%. a Symptomatic cases; b cases with acute otitis media (AOM; percentages of symptomatic cases in the “no risk” group: 0–1 year: 39.7%, 2–6: 19.6%, 7–12: 4.4%, 13–17: 4%, 18+: 1%; in the risk group: 1% [–35]), (c) deaths due to influenza (percentages of symptomatic cases in the “no risk” group: 0–1 year: 0.062%, 2–6: 0.027%, 7–12. 0.011%, 13–17: 0.005%, 18+: 0.0132%; in the risk group: 0.13%, guided by [36, 37]). For numerical results, see Additional file 1: Table S3

Fig. 6

Schematic figure of direct and indirect effects of pediatric vaccination. The upper boxes depict children, the lower ones adults. Boxes on the left show the baseline situation without additional vaccinations; on the right, 20% of children is vaccinated with a vaccine efficacy of 80%. Black areas show infected individuals, dark grey areas show vaccinated individuals. The shaded part of the vaccinated individuals depicts children who would have been infected and are, thus, directly protected. Preventing these cases also reduces the infection rate for unvaccinated children and for adults, causing indirect effects depicted in light grey