### Abstract

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

**Objectives: ** Influenza surveillance systems have been established in many countries in the world, yielding timely information about the intensity and features of seasonal outbreaks. Such data have also been used to estimate epidemiological parameters and to evaluate the effect of factors on infection dynamics. However, little is known about the extent of under-reporting in surveillance data, and thus of the true influenza incidence in the population.

**Design: ** Through mathematical and statistical modelling, we analysed Italian epidemiological and virological surveillance data collected together with serological data derived from influenza vaccine clinical trials performed in Italy.

**Results: ** Depending on the season, the reporting rate estimates ranged between 20% and 33% of the total incidence with higher reporting rates in seasons dominated by A/H3N2 virus. Despite a generally higher number of individuals immune against A/H3N2 viruses, effective reproduction ratios were quite similar in all seasons varying between 1·2 and 1·4. We observed an age-dependent transmissibility for different subtypes: susceptible children were more likely than susceptible adults and elderly to get infected when A/H1N1 or B strains were circulating, while no clear age-dependence was found for A/H3N2. We also perform sensitivity analysis under different assumptions for vaccine effectiveness, generation time (GT) and model variants; we found that the overall results in predicted patterns were extremely similar, with a slightly better fit obtained with shorter GTs.

**Conclusions: ** Our results provide relevant information on the influenza dynamics to fine-tune intervention strategies and for data collection improvement.

### Introduction

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

Owing to the substantial morbidity and mortality impact^{1} of influenza epidemics and also to their economic burden,^{2} their containment has become a major public health goal. Surveillance programs have been established in many countries in the world,^{3} and data are regularly collected during seasonal outbreaks. Such data have been used to estimate crucial epidemiological parameters,^{2,4} to forecast or simulate the dynamics of these epidemics,^{5,6} to evaluate the effect of specific factors or interventions on the disease dynamics.^{7–9} However, it is generally believed that the surveillance systems underestimate the true number of cases,^{10} and little is known about the extent of under-reporting.

During the 2009/2010 pandemic season, the importance of monitoring influenza activity has been emphasized because the existing surveillance system in Italy was not sufficient to describe the pandemic. In fact, a number of additional surveillance systems were developed in Italy to provide a more complete picture of influenza.^{11}

For this reason, we have analysed the dynamics of seasonal influenza in Italy before the pandemic spread, using data derived from the national sentinel surveillance system (epidemiological and virological), coupled with data on susceptibility derived from influenza vaccine clinical trials conducted at the national level. By a joint analysis of these two data sets, we have estimated age-specific transmission rates, levels of immunity in different age groups and reporting rates, and derived an estimate for the basic reproductive ratio.

### Discussion

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- References
- Supporting Information

We have analysed the spread of influenza in Italy during the last decade, integrating the data coming from the INFLUNET system, from the virological surveillance system coupled with the results of serological tests conducted at the national level. The estimated parameter values obtained from our analysis may help to gain a deeper insight into the dynamics of the seasonal influenza infections.

One key factor in determining these dynamics is certainly population susceptibility. Estimates of the fraction of susceptible individuals, varying between 25 and 100%, are available in the literature,^{6,9,31,32} but, up to our knowledge, there are no estimates based on a joint analysis of incidence and serological data as performed in this study. Our model assumes that individuals are either immune or not, even if in reality they could be partially immune to a subtype after a contact with a similar virus. Moreover, our model does not account for any possible decay in antibody levels over the summer period. However, widespread evidence suggests that the decay is limited in a few months span (3–6 months),^{33} and for this reason, we decide not to include a new parameter basically unidentifiable through the available data. With this caveats, the estimated initial fraction of susceptible is very high (about 100%) in children (0–14), and lower for the other age groups, ranging between 30 and 82%, in adults (15–64) and from 20 to 46% in elderly (64 and over). This is in agreement with the results of the previous studies^{4,34} and with the epidemiology of influenza: in fact, adults, and especially elderly, are more likely to have a partial immunity to the circulating strain, because of the previous contacts with similar viruses.^{35,36} Moreover, these estimates include the effect of vaccination, with about 60% of people older than 65 being vaccinated at the beginning of each season.^{15}

An estimate of 100% susceptibility in children may be considered implausible, as a reasonable proportion of them will have had multiple influenza exposures. First of all, one may note that often the same strains had not circulated for several years before the season under study, so that exposure to the same antigen may had been rare. Still, the extreme estimate of 100% appears unlikely biologically and presumably is selected by the model to account for the much higher reported incidence in children than in adults, because the lack of serological tests in children does not set any constraints to susceptibility levels. Possibly, this could be corrected by allowing for a higher reporting rate in children than in adults (while our model assumes, as stated above, constant reporting rate) and/or for the possibility that serological tests underestimate the actual degree of protection existing in the population. However, we had no independent data to verify these hypotheses; adding more unknown parameters would have made the models unidentifiable.

A comparison with the susceptible fractions estimated from serological data (when available) shows that, except for few values, there is a very good correspondence between the data and the estimates. A relevant discrepancy between observed and predicted values is found only in season 2002–2003, when the observed changes in seroprevalences differ from what could be gathered from the reported flu incidences. In this case, we could say that the dynamical model corrects the serological measures into the epidemiological relevant quantities.

In our model, we did not couple outbreaks in different years, only one season at a time is considered. However, seasonality is a driving force that has a major effect on the spatio-temporal dynamics of influenza transmission.^{37} Recently, a forced SIR epidemic model has been recognized to be able to identify a new threshold effect, taking into account the population’s susceptibility measured after the last outbreak and the rate at which new susceptible individuals are recruited into the population to give clear analytical conditions for predicting the occurrence of either a future epidemic outbreak or a ‘skip’ a year in which an epidemic fails to initiate.^{38} This is something that should be better investigated in the future.

In our model, we allowed for a difference in ‘susceptibility’ (i.e. probability of acquiring the infection if exposed) among the individuals of different ages. According to our hypothesis, a strain to which individuals are more susceptible can be considered more transmissible. Our analysis suggests that A/H3N2 is generally more transmissible than A/H1N1 and B viruses, especially to adults and elderly. In fact, while for A/H1N1 and B transmissibility to children is about twice as large as in other age groups, for A/H3N2 transmissibility to adults and elderly is as high as to children in two of the three analysed seasons. Our results are in overall agreement with the previous studies.^{9,31,39–41} A study by Pérez-Trallero *et al.*^{42} shows that all age classes get infected more often with A/H3N2 than with A/H1N1, possibly due to less frequent antigenic mutation in the latter, but this is especially true for elderly, possibly because of old antigenic memory. Moreover, recent studies on 2009 pandemic have shown that even the large diffusion of the pandemic virus in youngest individuals, many, of all ages, remained susceptible after the main 2009 wave in Hong Kong and Italy.^{43,44}

The issue of reporting is one of the limits of the influenza surveillance system, because of the impossibility to monitor the occurrence of influenza in those individuals who do not seek medical assistance. The risk associated with this limit is an underestimation of influenza incidence rates in the community. The subtype-specific reporting rate estimated in our analysis is higher for A/H3N2 (varying between 18 and 30% for the three selected seasons) and slightly lower for B (between 16 and 22%) and A/H1N1 (around 17%). In general, available estimates vary between 12·5%^{45} and 50%^{9} and are consistent with our values. Our estimates provide a first measure of evaluation of the surveillance system, which is commonly believed to underestimate the true number of cases.^{10}

We have assumed that reporting rates do not vary with age, which could represent an alternative explanation to the observed differences in population susceptibility. Indeed, Xia *et al.*^{46} had pointed out that elderly are more likely to visit their GP when infected. To have model predictions with equal ‘susceptibilities’ compatible with actual notifications, one would have to assume that A/H1N1 and B cases are notified more often among children than among adults and elderly, while A/H3N2 are notified equally among all classes. The present data do not allow us to exclude this hypothesis; more extensive serological data, including also children, would be needed for that.

An interesting result of our analysis that is not affected by these uncertainties is the estimation of strain-dependent effective reproductive ratios, with values ranging from 1·2 to 1·4. Earlier studies^{9,31} proposed similar estimates. As mentioned above, these estimates depend on the assumed length of GT; clearly, allowing for uncertainty in this would result in wider confidence intervals for *R*_{0}.

The same type of analysis could be extended to all other seasons, but the lack of relevant immunological data prevents the use of the same methods. To perform the analysis without serological data, one could assume that reporting rate and transmissibility are intrinsic property of a (sub)type and do not change with antigenic drift, but our analysis suggests that this is not the case, especially for (sub)type A/H3N2. Another problem concerns those seasons in which two or more strains co-circulated, for which further results on the potential role of short-term cross-protection^{46,47} would be of great value.

Our model reproduces the observed dynamics of influenza remarkably well; a possible extension of our analysis could include spatial heterogeneities or, given the importance of transmission in children,^{9} school holidays. A statistical analysis of the potential influence of school holidays and temperature patterns on transmission is underway.

Despite the model limitations, our results provide important information on the dynamics of influenza and estimates of subtype-specific parameters that may be useful to calibrate intervention strategies or to improve data collection.