Influenza A evolves over time, escaping the immunity of human host populations [1]. As a result, individuals are exposed to a range of different strains over a lifetime, and different age groups have varying levels of antibodies to particular strains, depending on which viruses they have seen. Several serological studies during the 2009 influenza pandemic also considered recent seasonal H1N1 and H3N2 strains, with haemagglutination-inhibition (HI) titres given for different age groups. Across a number of countries, the data all follow a distinct pattern [2], [3], [4], [5], [6], [7], [8]: a high proportion of individuals are seropositive (HI titre>40) in adolescence, followed by a clear decrease in seropositivity between adolescence and age 60–65, before a rise in the older ages.

Heterogeneity between age groups has been much studied in an epidemiological context [9], [10], and recent work used serological data for varicella and parvovirus to infer transmission rates between age groups [11]. However, despite the increasingly availability of social contact data [12], [13], it has previously been difficult to compare mathematical model outputs with data from serological studies for seasonal influenza: the proliferation of variables required as the number of strains in the model increases makes it technically challenging to look at the long term impact of different assumptions.

Progress has recently been made by introducing age structure to a multi-strain model, allowing the effect of influenza dynamics on population immunity to be examined in more detail [14]. Here, an extended version of this model is used to examine the possible causes of the unusual age distribution of seropositivity to seasonal influenza A in humans. A number of candidate factors are included: basic reproductive ratio (); heterogeneous mixing between age classes; cross-immunity between strains; vaccination effectiveness. We also consider ‘original antigenic sin’ (OAS) [15], a theory that suggests that previous infection dominates subsequent immune responses: rather than develop antibodies to every new epitope that is encountered, if strains are antigenically similar, the immune system may reuse antibodies previously raised against the epitopes of an old strain, instead of developing immunity to the novel ones.

A simulation-based maximum-likelihood analysis is used to quantitatively compare the consequences of different assumptions with serological data from Australia [2] and Finland [3]. The data are compared with the degree of immunity calculated in the model by imposing the assumption that individuals with HI titre >40 are immune, and do not transmit infection. Although the precise relationship between the two is unclear, it has previously been shown that an HI titre >40 correlates with protection [16], [17].

This framework is used to assess the contribution of the different candidate factors. In particular, we see that if mixing follows physical interactions seen in social contact data and OAS is included in the model, it is possible to recreate the patterns seen in these serological studies.

Using this framework, we tested combinations of three different assumptions: 1) transmission derived from physical contacts or conversational contacts in the POLYMOD survey [13]; 2) clusters of strains or fixed amount of antigenic change each year; 3) OAS or no OAS. The eight possible models were compared using the AIC, corrected to avoid overfitting [33]. Table 2 shows that the model with physical contacts, OAS and clusters gave the best fit according to the AIC. In addition, the values of , which give the difference in AIC compared to the best fitting model, suggest that models with transmission based on conversational contact data [13] all have less support under the AIC than those based on physical contacts. Figure 1 compares the six sets of data with the maximum likelihood fit of model 1, which best explained the data. The model captures the general shape of five of the data sets, in particular the drop in seropositivity after adolescence, but does not fit as well to the Australian data for H3N2/Brisbane/07 (Figure 1F); the substantial drop in immunity after childhood does not occur in the model.

The decrease in seropositivity between the second and third age cohort is present in all datasets except Figure 1E. We propose that this is caused by the changing influence of OAS with age, as shown schematically in Figure 2. In the youngest age groups immunity gathers with infection: each exposure leads to an increased antibody repertoire. At the population level, this causes an increase in seropositivity with age. However, once a large proportion of individuals have been infected with at least one strain, OAS starts to have an effect, with subsequent infections re-stimulating existing antibodies rather than novel ones. The virus is still evolving, however, so the effective immunity to a new strain decreases with age until the virus is sufficiently different for the immune response to escape the effect of OAS, enabling an increase in immunity in older age groups. The maximum likelihood point estimate for the reach of OAS, , was 0.93. This implies that OAS can occur even if there is only a small degree of cross-reaction between strains, and that the preferential utilization of childhood immunity continues well into adult life. Based on our estimates for and (Table S2), and assuming cluster change every 4 years on average for H1N1 and 3 years for H3N2 (Table S1), the temporal reach of OAS in the model ranges from 22–47 years.

For individuals who have seen at least two strains, the parameter estimates from model 1 suggest that, on average, the time between seeing the first and second strain is 6.0 years (details in Text S1). The overall average time between infections for each age class is given in Figure S2, with children seeing infection more often than older age groups.

Figure 3 shows the estimated degree of cross-immunity between clusters of strains, based on estimates in Table S2. Both subtypes have a similar decay over time, but the best fitting model suggests that H3N2 generates a noticeably higher degree of cross-immunity than H1N1; this parameter fit is a result of the large proportion of individuals seropositive to H3N2 in Finland (Figure 1D).

The estimates for and are shown in Table 3, with 95% confidence intervals in brackets (see Text S1 for details); these are slightly lower than previous estimates for , based on observed epidemic data [34], [35]. Note that data from Norway and France are shown for comparison, as published estimates for Finland could not be found.

Using a multiple strain epidemic model, we have examined the age profile of immunity seen in serological data for seasonal influenza A in humans. Of the models considered, we have shown that the patterns observed in these studies can be best explained with a model which includes transmission based on physical contacts, antigenic clusters and original antigenic sin.

Although the model reproduces the general shape of much of the data, it does not fit as well to the Australian data for H3N2/Brisbane/07 (Figure 1F): there is a substantial drop in immunity after childhood that is not captured. This could be owing to a combination of factors. Some of these would be inconsistent with the other data, such as a higher rate of evolution (i.e. larger ) in Australia than in Finland. Others, such as a specific feedback over time between and virus evolution, would require numerous extra parameters, reducing the parsimony of the model. There may also be a discrepancy between the proportion of individuals with HI titre >40 and the true level of population immunity [16], [17], whereas we have assumed that individuals who are seropositive do not transmit infection. Microneutralisation assays provide a more sensitive and more specific method of measuring immune response than HI assays [36], however a correlate of protection has not yet been established for such tests [37]. The relationship may also be further complicated if in reality immunity offers clinical, but not transmission-blocking protection. A discrepancy between seropositivity and immunity may explain the difference in level of cross-protection between H1N1 and H3N2 strains in Figure 3.

Our results, which reproduce the decline in seropositivity between adolescence and middle age, are consistent with OAS occurring in combination with antigenic change in the virus. The effect is illustrated by level of immunity to H1N1/New Caledonia/99 (Figure 1B). Vaccine updates [25], [26] indicate that this strain was in a cluster that circulated until around 2006. However, in 2009 school children had the highest level of immunity to this virus, even though young adults would have been in the high-transmission school environment when this strain originally appeared in 1999. The first infection of a young adult would likely have been with a pre-1999 strain, though, so original antigenic sin could have subsequently inhibited the creation of specific immunity against New Caledonia/99 during these individuals' school years. This would not have been an issue for children born post-1999.

The maximum likelihood estimate for the reach of OAS, , in the best-fitting model was 0.93. This suggests that childhood immunity dominates even if there is only a small degree of cross-immunity between strains. If antigenic evolution occurs at the rate suggested by the decay in Figure 3, this would mean that OAS still influences immunity several decades into an individual's life. OAS is likely caused by competition between existing memory B cells and naive ones for antigen [38], [39]. The estimate for therefore suggests that even if persisting antibodies to the first strain seen have limited effectiveness against the epitopes of the current virus, they still prevent the activation of naive B cells, which would produce more effective antibodies [39]. If antigenic sin can recur, with memory B cells formed later in life also outcompeting naive ones, then a smaller reach would be required to generate a drop in immunity in middle age groups [14]. The increase in immunity in the elderly (Figure 2) would no longer be observed either; as subsequent strains could also induce antigenic sin, there would no longer be an age at which individuals could ‘escape’ its effects. Further studies into OAS could help address this issue. By examining the within-host interaction between B cells that likely generates antigenic sin, it would become clearer whether our simple version of OAS is sufficient in models of population immunity, or if a more detailed set of assumptions – such as the recently proposed ‘antigenic seniority’ hypothesis [40] – is required.

If antigenic sin could recur, it would also have implications for the inference of vaccination effectiveness, . Using model 1, which assumes OAS, we estimated to be 6% for H1N1 and 24% for H3N2. A meta-analysis of empirical work into vaccine effectiveness [41] suggested vaccination reduced ILI by 35% (95% confidence interval 19–47%), and a review of vaccine efficacy [42] suggested a value of 17–53% for clinical efficacy in the elderly. Our estimates are low compared to these values. However, in our model is defined as the additional reduction of transmission provided by vaccination, so its inferred value depends on the level of existing immunity in the elderly; if antigenic sin could recur, then the elderly would gain less natural immunity [14], and so we would expect the fitted value of to increase.

Vaccination is implemented by removing a fixed proportion of the elderly from the compartment at the start of each season. Cross-protection can therefore be considered by interpreting as the protection conferred from that season's vaccine as well as cross-immunity from previous years' campaigns. As a result, we would not expect the introduction of explicitly cross-protective vaccine (i.e. one that also removed individuals from future compartments) to substantially change our results, other than the estimate for . Interestingly, an increase in seroprevalence in older age groups has also been observed in populations with few vaccinated individuals [43], which suggests it may not be vaccination alone that is responsible for the rise in the elderly outlined in Figure 2.

The estimates for the effective reproductive ratio, , given in Table 3 are lower than estimates obtained in epidemiological studies. However, it is worth noting that the real-life estimates for France and Australia [34] did not include mild epidemics, whereas here is estimated from values of calculated for each year. As such, confidence intervals for can extend below one if epidemics do not occur in every year of the simulations, as happens for H3N2. The estimates in Table 3 also suggest that there may not always be an easily discernible relationship between , which can be estimated from data [34], [35], and , which often cannot. H3N2 in Finland has the largest fitted , yet a high transmission rate results in a large degree of immunity, reducing .

Several assumptions have been made in the model presented here. We assume that immunity reduces transmission, rather than susceptibility: antibodies from past exposures do not prevent an individual from acquiring new infections – and adding these strains to their infection history – but they may prevent that person from transmitting the infection to others. Whereas a simple mechanism is used to represent OAS in the model, in reality factors such as cross-reaction, OAS and are likely to be subject to additional variation – both within-host [38] and at the environment level [44] – that is not included in the framework we have outlined here. In addition, transmission rates between age groups were based on age mixing data from the POLYMOD survey [13]. It has previously been shown that a model based on physical contacts from POLYMOD fits well to serological data for varicella and parvovirus [11], and our results suggest the same for influenza: it appears that transmission based on physical contacts captures influenza dynamics better than that based on conversational interactions. When conversational contact data is used in the model, much transmission occurs amongst the eldest two age classes; with physical contact data this bias is smaller, with more transmission to and from the younger classes. Further research into the role of school children [12] – who display a large amount of immunity relative to other age groups – in transmission might provide the detail required to better understand why physical contacts appear to be more relevant than conversational ones. Finally, we have only fitted the model to data from two studies: if more data on seropositivity to seasonal strains were to become available it might help elucidate some of the above issues. It may also improve our understanding of seasonal epidemics; although the effect of the immune structure of a population on an outbreak is well documented for pandemics [37], [45], it has been suggested that previous infections can have counter-intuitive implications for epidemic dynamics, with OAS leading to ‘blind spots’ in immunity [14].

To our knowledge, this is the first time a high-dimensional model of disease strains has been quantitatively compared with serological data for seasonal influenza. As well as highlighting the role played by age-dependent mixing and original antigenic sin, our work suggests that there may be an additional mechanism involved in shaping population immunity still to be identified. Further empirical studies into the immune structure of a population, interfaced with strain models such as the one presented here, are therefore essential if we are to fully understand how individuals build immunity to diseases like influenza.