Study population and design

This study uses data from two household influenza transmission studies based in Managua, Nicaragua: the Household Influenza Transmission Study (HITS) and the Household Influenza Cohort Study (HICS). HITS is a case-ascertained study, meaning that influenza-positive individuals are identified, and other members of their household recruited for enrollment, that ran from 2012 to 2017, and HICS is a prospective household-based cohort study that began in 2017 and is currently ongoing. In both studies, influenza A/H3N2 virus-positive individuals, the index cases, are initially detected at a health center, where household members are enrolled (HITS) or activated (HICS) into intensive monitoring for a period of ~14 days. During this period, household members are tested repeatedly for influenza virus, allowing for a reconstruction of likely transmission chains within each household. Blood samples are collected both at the beginning of the monitoring period, no later than 7 days after symptom onset or household activation, and 30–45 days after³⁸. Prior work using this population has focused on ascertaining correlation between various antibody responses and protection against infection. This analysis expands on that work by modeling protection against infection utilizing more sophisticated household transmission modeling, as well as modeling the association between antibody measurements and infectivity²⁸. These studies were approved by the institutional review boards at the Nicaraguan Ministry of Health/Center National of Diagnosis and Reference Institutional Ethics Review Committee (Code NIC-MINSA/CNDR CIRE-05/04/17-080 Rev 13) and the University of Michigan (IRB Approval # HUM00119145) and are in accordance with the Helsinki Declaration of the World Medical Association. Written consent to participate or parental permission was obtained for all participants; in children older than 6 years, verbal assent was obtained. Data on gender were collected from participants using self-reports. Data were not stratified by gender for foundational models, given limited statistical power and the absence of compelling prior evidence that the association between antibody levels and infectivity differs by gender. Data were collected via trained study personnel conducting home visits utilizing tablets to import survey data. Data were collected on all individuals enrolled in the study who met criteria for an intensive monitoring period, so sample size calculations were not performed.

Laboratory methods

Nasal/oropharyngeal swabs collected from household members were tested for influenza virus with real-time reverse-transcription polymerase chain reaction (RT-PCR) using validated Centers for Disease Control and Prevention (CDC) protocols. If positive for influenza virus, subtype or lineage determination was performed using additional RT-PCR assays^39,40,41. Pre-transmission antibody levels were assessed by testing each sample using (1) HAI along with enzyme-linked immunosorbent assays (ELISAs) directed at antibodies against (2) full-length HA, the (3) HA stalk, and (4) NA. HAIs were performed to test the ability of participant antibodies to neutralize influenza virus HA’s agglutination of turkey red blood cells, a proxy for antibody responses against the HA head. ELISAs were performed to test participant antibody responses against full-length HA, the HA stalk, and NA. The HAI of samples against A/Hong Kong/4801/2014 was tested. Immunoglobulin G (IgG) antibodies against trimeric H3 A/Hong Kong/4801/2014 and tetrameric N2 A/Hong Kong/4801/2014 were measured by ELISA using an anti-human IgG (Fab specific) horseradish peroxidase detector⁴². Antibody responses against the HA stalk were measured using a cHA (cH7/3) protein that expresses a head domain to which participants should be naive (A/Anhui/1/2013) along with the stalk of H3 (A/Hong Kong/4801/2014), ensuring that detected immune responses against the cHA are directed at only the HA stalk. The analyses utilized assay data from initial, baseline samples, which were collected either before or shortly after household activation, when anti-influenza IgG levels should approximate preexposure levels. Sera were treated with receptor-destroying enzyme and incubated overnight at 37 °C. Following inactivation and dilution in saline, 50 µL of inactivated sera were added to the first column of a 96-well V-bottom plate, and a two-fold serial dilution was performed across columns 1–10 (final dilutions ranging from 1:10 to 1:5120). Influenza virus antigen was added to columns 1–10, and 0.5% turkey red blood cells were then added to all wells. Hemagglutination inhibition was read after 30 min of incubation at room temperature. The HAI titer was defined as the reciprocal of the highest serum dilution that completely inhibited hemagglutination.

We used only RT-PCR assays to avoid potential bias that could arise from using serology, as individuals with high pre-existing antibody levels, which are the focus of this study, might have a higher probability of being classified as infected. In total, 113 of 516 (21.8%) PCR-negative individuals exhibited a fourfold or greater rise in HAI titers, possibly reflecting a host immune response to circulating household infection in individuals who do not develop an explicitly RT-PCR positive infection. These individuals would likely be classified as an infection under a less stringent definition, which reflects the imperfect specificity of HAI compared to RT-PCR as the gold standard. Several serological assays were conducted on each blood sample to measure the initial and final antibody levels against various influenza antigens; hemagglutination inhibition assays (HA heads), and enzyme-linked immunosorbent assays (ELISAs) against full-length HA, the HA stalk, and NA. Details about the specific antigens used for each assay are available in the supplement (Table D1).

Recombinant antigen proteins were diluted in 1× phosphate-buffered saline (PBS) to a final concentration of 2 μg/mL. A 50 μL volume of each antigen solution was added to 96-well microtiter plates (Immulon 4 HBX; Thermo Scientific, cat. no. 439454) and incubated overnight at 4 °C. Plates were washed three times with PBS-T (1× PBS containing 0.1% Tween 20) using an automated plate washer (BioTek 405TS). Blocking was performed with 200 μL/well of 3% (w/v) non-fat milk powder in PBS-T for 1 h at room temperature (RT). After removing the blocking buffer, heat-inactivated serum samples (mouse or human) were serially diluted in 1% (w/v) milk-PBS-T, starting at a 1:100 dilution, followed by twofold dilution steps and incubated for 2 h at RT. Plates were subsequently washed three times with PBS-T.

Anti-human IgG (Fab-specific)-HRP (Sigma-Aldrich, A0293; 1:3000) diluted in 1% milk-PBS-T was added (50 μL/well) and incubated for 1 h at RT. After plates were washed three times with PBS-T, 100 μL/well of o-phenylenediamine dihydrochloride (OPD; SIGMAFAST) substrate was added. The reaction was stopped after 10 min with 50 μL/well of 3 M HCl (ThermoFisher). Optical density (OD) at 490 nm was measured using a BioTek Synergy H1 or Synergy 4 plate reader.

Area under the curve (AUC) was calculated to quantify total antibody binding across serial dilutions. OD values at each dilution were plotted against dilution factor, and the AUC was determined by integrating the curve using GraphPad Prism software.”

Statistical methods

Descriptive statistics of the study population are presented in Table 1. For categorical variables (e.g., gender, vaccination status, season), the number of individuals and their proportions are reported for each category. P values are calculated using a chi-squared test of independence to determine whether the proportions significantly differ between the infected and noninfected groups.

For continuous variables (e.g., age, antibody levels), we report the median and standard deviation within each group (infected and non-infected). The Mann–Whitney U test is used to assess whether the distributions of these variables differ significantly between the two groups, as this test does not assume a parametric distribution. This test is robust to left-censoring of observations, as it relies on the relative ranking of the data rather than their absolute values. P values < 0.05 are considered statistically significant, indicating a difference in distributions at a 5% risk level.

We performed a first regression analysis using boosted regression trees to assess the association between the age and antibody titers of the index case and household contacts and the probability of infection in the household contacts. Boosted regression trees were chosen because they can capture non-linear relationships in the data and account for potential interactions between variables^43,44,45.

The XGBoost algorithm was used to partition the co-variate space defined by antibody levels and age and to assign each subspace a corresponding probability of infection. To minimize the risk of overfitting, we implemented 5-fold cross-validation⁴⁶. The optimal number of boosting rounds (iterations) was selected using early stopping, ensuring the model stops training once further iterations do not improve performance on the validation set.

We present the estimated association of each covariate with the probability of infection, along with confidence intervals derived using a bootstrap procedure. Specifically, we resampled 80% of the training set 500 times and re-estimated the model parameters for each resampling.

To evaluate global co-variate importance, we used the mean absolute SHapley Additive exPlanations (SHAP). SHAP values measure the average contribution of each covariate to the prediction⁴⁷. For a given observation i, the SHAP value i, ϕ_ij for covariate j represents the marginal contribution of that covariate, averaged across all possible combinations of covariates. The mean absolute SHAP value quantifies the overall importance of a covariate while ignoring the directionality (sign) of its effect.

Finally, we computed the p-value associated with each variable using a permutation test⁴⁸. To perform this test, we randomly permuted the observations and computed the mean absolute SHAP value for each permutation. We then compared the proportion of permutations in which the mean absolute SHAP value exceeded the real SHAP value. If the observed SHAP value is consistently larger than the permuted SHAP values, it indicates that the covariate has significant importance in predicting the outcome beyond what would be expected by chance.

Analyses were conducted using R version 4.2-4.5.0 and Visual Studio Code version 1.82.0-1.104.

Transmission model and analysis

We used a mathematical model to assess the impact of individual-level age and immune characteristics on the person-to-person probability of transmission. The model estimated the risk of transmission between all household members, including the risk from secondary cases. We modeled how the risk of transmission from an infected individual varied according to time after infection with a gamma distribution^24,49,50,51 with a median at 3.5 days and a standard deviation of 2 days. This transmission risk was modulated by infectivity factors, including the infected individual’s pre-existing antibody titers against HA head, HA stalk, and NA. It was further influenced by susceptibility factors, which comprised the characteristics of the susceptible contact, namely their age and pre-existing antibody titers (anti-HA head, anti-HA stalk, and anti-NA). Household size was also included as a covariate. Additionally, we estimated a baseline risk of infection from the community. Compared to traditional approaches, such as logistic models^24,31,51,52, a key advantage of our transmission model is that it can simultaneously account for transmission risks from the index case, other infected household members, and external community sources. Full details of the transmission model are provided in the Supplementary Information.

We estimated how transmission risk was modulated by individual antibody titers. For each antibody type, we estimated two pairs of parameters: one pair quantifying the reduction in infectivity and another pair quantifying the reduction in susceptibility. The first parameter represented the threshold antibody level at which infectivity or susceptibility was reduced, and the second quantified the associated reduction in transmission. Reductions in susceptibility, reductions in infectivity, and their corresponding antibody thresholds were jointly estimated within the transmission model.

Inference framework

Inference is complicated by the fact that times of infection are not observed. We used a Bayesian data augmentation approach to address this missing data issue^24,53. In this framework, unobserved times of infection are considered as “augmented data” and the joint posterior distribution of transmission parameters and augmented data is explored by Markov chain Monte Carlo (MCMC). The statistical model had a hierarchical structure with three levels: (i) the observation level ensures consistency between observed and augmented data based on the probabilistic distribution assumed for the incubation period^54,55,56. The incubation period is modeled as a log-normal distribution with a median of 1 day and a standard deviation of 1.2 days. (ii) the transmission model (described above), characterizes within household transmission dynamics, (iii) the prior model describes prior distribution for model parameters. They are reported in the “Priors of the Reference Transmission Model” section of the Supplementary Information. Transmission parameters and augmented times of infection were iteratively updated using a Metropolis-Hastings algorithm ^24,53,57. Each MCMC chain was run for 50,000 iterations, with the first 10,000 iterations discarded as burn-in. We report the median of the posterior distributions along with the 95% credible intervals (CrI) for each estimated parameter. Convergence was assessed using the Gelman-Rubin diagnostic (\({\hat{R}}\)) and reported the values in Table S15.

The prior for relative risks was specified as a log-normal distribution with a log-mean of 0 and a log-standard deviation (log-SD) of 1. The baseline threshold priors were informed by visual inspection of results from boosted regression trees. For susceptibility, the threshold prior was specified as a uniform distribution from 10 to 70. For infectivity, the NA threshold was assigned a uniform prior from 10 to 50, and the HA stalk threshold from 40 to 70. More details are reported in the supplement.

Sensitivity analysis

In our baseline model, we assumed that the effects of different types of antibodies on susceptibility and infectivity were additive. In a sensitivity analysis, we assessed this assumption by evaluating the combined effects of high antibody levels across multiple antigens. Using the thresholds estimated from the baseline model, we categorized individuals as having high or low antibody levels for infectivity and susceptibility analyses. For susceptibility, we evaluated the effect of: (i) a single high antibody level; joint high levels of two antibodies (HA head and HA stalk; NA and HA stalk; NA and HA head); combined high levels of all three antibodies. For infectivity, we excluded HA head due to its lack of association with reduced infectivity and assessed the reduction associated with high levels of NA only, HA stalk only, or their joint high levels.

We performed sensitivity analyses on prior assumptions related to viral life history traits, including the incubation period and generation time distributions. In the baseline model, we assumed a generation time with a mean of 3.5 days and a standard deviation of 2 days. Alternative scenarios included a shorter generation time (mean = 3 days, SD = 1.5 days) and a longer one (mean = 4 days, SD = 2 days). The baseline incubation period was set to a mean of 1 day with a standard deviation of 1.2 days. We also tested a shorter incubation period (mean = 0.6 days, SD = 0.8) and a longer one (mean = 2 days, SD = 1.6).

In a sensitivity analysis, we tested a wider prior with a log-SD of 2 for relative risk parameters. We also performed sensitivity analyses on the priors for the antibody titer activation thresholds. We tested uniform priors centered around the target thresholds with varying widths of 20, 40, 60, and 80. For example, with a width of 20, the priors were set to 25–45 for susceptibility, 20–40 for NA infectivity, and 50–70 for HA stalk infectivity.

Model validation and simulation

To validate the model, we generated 2000 datasets of infection events using an agent-based model. The simulations preserved the household structure, index case assignment, and individual characteristics such as age and antibody levels. At each time step, infection events were randomly sampled based on the probability of transmission derived from the transmission model, using the posterior medians of the estimated transmission parameters.

Model adequacy was assessed by comparing the secondary attack rates (SARs) across different household sizes between the simulated datasets and the observed data. To evaluate parameter identifiability, we calculated the proportion of the posterior distribution that included the simulation-derived parameter values within the 95% credible interval (CrI). A proportion close to 95% ensures that the parameter is well identifiable.

All analyses were performed, R (versions 4.3.1–4.3.2), Visual Studio Code (version 1.87.2) and Python 3.13.0 for the XGBoost analysis.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.