Variation in loss of immunity shapes influenza epidemics and the impact of vaccination

Background: Protective antibody immunity against the influenza A virus wanes in 2-7 years due to antigenic drift of the virus' surface proteins. The duration of immune protection is highly variable because antigenic evolution of the virus is irregular. Currently, the variable nature of the duration of immunity has had little attention in analyses of the impact of vaccination, including cost-effectiveness studies. Methods: We developed a range of mathematical transmission models to investigate the effect of variable duration of immunity on the size of seasonal epidemics. The models range from simple conceptual to more realistic, by distinguishing between infection- versus vaccination-induced immunity, by inclusion of primary vaccine failure, by assuming a leaky vaccine, and by the inclusion of age-dependent contact patterns. Results: We show that annual variation in the duration of immunity causes large variation in the size of epidemics, and affects the effectiveness of vaccination. Accumulation of susceptible individuals in one or more mild seasons results in a disproportionately large outbreak in a subsequent season. Importantly, variation in the duration of immunity increases the average infection attack rate when the vaccination coverage is around the outbreak threshold. Specifically, in a tailored age-stratified model with a realistic reproduction number (R ₀ = 1.4) and vaccination coverage of 25%, we find that the attack rate in unvaccinated children (<10 years old) is negligible if the duration of immunity is constant, while on average 2.8% (2.5-97.5% percentiles: 1.8-4.1%) of the children are infected if the duration of immunity is variable. These findings stem from the buildup of susceptibility over multiple seasons by waning of immunity, and the nonlinear relation between susceptibility and infection attack rates. Conclusions: The models illustrate that variation in the duration of immunity impacts the long-term effectiveness of vaccination, and that vaccine effectiveness cannot be judged for each year in isolation. Our findings have implications for vaccination strategies that aim to maximize the vaccination coverage while extending the age range of persons eligible for vaccination.