Multi-source agent-based modeling to optimize influenza mitigation strategies in Hong Kong

Abstract

Seasonal influenza control faces challenges from variable vaccine effectiveness and uncertain non-pharmaceutical intervention (NPI) performance. While vaccination remains the primary strategy, its effectiveness varies between vaccine-matched and mismatched seasons. Increased post-COVID-19 NPI acceptance enhances influenza control feasibility, yet optimal combination approaches remain poorly understood. We use an agent-based model to analyze influenza transmission across six seasons in Hong Kong (2009-2013) with varying epidemic characteristics. We integrate surveillance, serological, and school absenteeism data for calibration, enabling accurate estimation of reported and unreported infections. We evaluate age-targeted vaccination, staying home when sick, mask use, and school-based interventions across diverse real-world scenarios. Compared to baseline, child vaccination consistently outperforms other strategies, with targeting those under 12 yielding the greatest population-level attack rate reduction (up to 8.5% relative reduction per 100,000 vaccinated). Among NPIs, 40% mask coverage reduces attack rates by 18%–43%, comparable to 25% of symptomatic individuals staying home. During vaccine-mismatched seasons, combining high-coverage mask use and staying home reduces attack rates by 79%–84%. High-coverage school-based vaccination is more effective than closures, reducing student attack rates by up to 85% versus 33% for 14-day closures. Our multi-source calibration approach provides robust evidence for prioritizing child vaccination and strategic NPI combinations.

Modeling six influenza seasons to evaluate mitigation strategies, this study proposes a signal-responsive policy framework. Findings show child vaccination and mask use curb transmission; their combination is vital during vaccine mismatches.

Introduction

Influenza remains a major global public health threat, particularly in subtropical and tropical regions, which typically experience multiple seasonal outbreaks each year¹. After the COVID-19 pandemic, influenza has experienced a resurgence worldwide². Hong Kong, a subtropical region, is significantly affected by seasonal influenza, with peaks commonly occurring from January to March/April and from July to August. In the post-COVID-19 period, influenza transmission in Hong Kong has returned to pre-pandemic levels, with outbreaks lasting even longer, up to 28 weeks, in 2024³.

Vaccination and non-pharmaceutical interventions (NPIs) are key tools against influenza, but their uptake and overall effectiveness remain uncertain. In Hong Kong, free seasonal influenza vaccination⁴ and a government subsidy program⁵ were introduced after the 2009 H1N1 pandemic for high-risk groups, including children under 6 and adults aged 65 and above. However, coverage remained low before 2014, with uptake rates of 12.9% and 32.7%, respectively⁶. The program has since expanded to include children under 18 and adults over 50. However, low perceived risk, safety concerns⁷, and shifts in public attitudes influenced by COVID-19 vaccination policies⁸ may have hindered progress in increasing influenza vaccine uptake in Hong Kong. Vaccine effectiveness is also challenged by mismatches with circulating strains⁹. Between 1996 and 2012, fewer than half of H3N2 seasons in Hong Kong had vaccine strains closely matching circulating viruses¹⁰, resulting in reduced protection.

NPIs such as social distancing¹¹, mask use¹², and school closures¹³ can reduce transmission, with COVID-19 experience having increased public acceptance and familiarity with measures such as mask use and work from home¹⁴. However, implementation remains constrained by economic costs¹⁵, logistical challenges¹⁶, and varying adherence across contexts¹⁷, underscoring the need for tailored strategies¹⁸.

Given these challenges with individual interventions, agent-based models¹⁹, offer valuable tools to assess optimal combination strategies by simulating transmission at the individual level. However, model reliability depends critically on calibration approaches that accurately capture true transmission dynamics. Common methods using surveillance data alone often underestimate infections due to underreporting and asymptomatic cases^20,21,22. These limitations necessitate integrated calibration using multiple data sources, including serological data²³, to improve model calibration and better capture true transmission dynamics.

To support the WHO’s Influenza Strategy 2030²⁴, we adapt an agent-based model to simulate influenza transmission in Hong Kong across six seasons (2009–2013). By integrating surveillance, serological, and school absenteeism data, we reconstruct baseline age-specific transmission dynamics and evaluate targeted interventions, including age-specific vaccination, staying home when sick, mask use, and school-based measures. This study provides context-specific evidence to guide seasonal influenza control and strengthen preparedness for future outbreaks.

Results

Overview

This study aimed to identify optimal strategies for reducing influenza attack rates in Hong Kong across diverse seasonal epidemic conditions, particularly vaccine-matched versus vaccine-mismatched scenarios. We evaluated the effectiveness of pharmaceutical and non-pharmaceutical interventions in reducing overall and age-specific infection rates during six influenza seasons (2009–2013), which varied in circulating virus subtypes, vaccine effectiveness, epidemic magnitude, and seasonal timing. Our analytical framework prioritized comparative assessment of targeted vaccination strategies, staying home when sick, mask use, and school-based interventions, both individually and in strategic combinations, to determine strategy effectiveness for different scenarios.

We used a stochastic agent-based model²⁵ to estimate influenza transmission dynamics in Hong Kong (Fig. 1). The model integrates diverse data streams to capture the heterogeneity of social contacts and infection progression within the population. A synthetic population was constructed using detailed demographic and social structure data, including age-stratified population figures, employment rates, enrollment statistics, and school capacity records, which informed the creation of realistic contact networks across multiple layers (households, schools, workplaces, and community settings). Infection time series derived from serological data, which captures both reported and unreported infections, avoiding the healthcare-seeking bias inherent in clinical surveillance, along with school absenteeism data, were used for model calibration, with the latter enhancing the representation of contact dynamics among school-age children.

Fig. 1.

Model structure.

Epidemiological characteristics of the six influenza seasons

The six modeled seasons (2009–2013) exhibited distinct epidemiological profiles (Table 1). Seasons 1, 2, and 6 coincided with summer holidays and showed predominantly H1N1 (season 1) or H3N2 (seasons 2 and 6) circulation. Seasons 3, 4, and 5 occurred outside summer holiday periods, with seasons 3 and 5 featuring well-matched vaccines and season 4 experiencing vaccine mismatch. Cumulative incidence of infections derived from serological data ranged from 0.29 million (season 6) to 1.25 million (season 4), with peak daily case numbers between 4518 (season 5) and 27,095 (season 4). The 0–24 age group had the highest or near-highest attack rates in five of six seasons, ranging from 4.5% to 34.6%.

Table 1.

Information on the six modeled seasons

Season	Season 1	Season 2	Season 3	Season 4	Season 5	Season 6
Start date	2009/06/20	2010/06/25	2010/12/04	2012/02/20	2013/01/01	2013/05/31
End date	2009/11/21	2010/10/16	2011/02/26	2012/06/23	2013/04/20	2013/10/12
Summer holiday	Yes	Yes	No	No	No	Yes
Variant	H1N1	H3N2	H1N1	H3N2	H1N1	H3N2
Vaccine matching	Mismatched	Matched	Matched	Mismatched	Matched	Matched
Cumulative infections (million)	1.24	0.96	0.75	1.27	0.30	0.29
Peak case number	27,090	18,127	21,456	27,095	4518	4532
Attack rate (%)
0–24	34.6	12.4	11.5	21.3	4.9	4.5
25–44	14.4	13.5	12.2	16.0	4.0	5.2
45–64	10.7	14.3	9.4	17.0	4.0	3.4
≥ 65	9.4	14.9	8.7	17.2	4.0	2.7
Peak influenza-related absences (per 100,000 students aged 6–18)	469	115	135	98	31	25

Smart-card-based school absenteeism monitoring revealed distinct temporal patterns that were moderately to strongly correlated with influenza activity (Fig. 2c; Pearson correlation = 0.40–0.95 across seasons). During high-transmission periods, peak influenza-related absenteeism among students aged 6–18 ranged from 25 to 469 per 100,000 student-days across seasons. Over the course of each influenza season, average daily absenteeism ranged from 8 to 53 per 100,000 student-days (Table 1).

Fig. 2. Model calibration results across six influenza seasons.

a New infection across six modeled influenza seasons. b Cumulative infection numbers. c Influenza-related school absences among students aged 6–18. d Age group distribution of infections. Across all panels, orange elements represent the observed empirical data used for model calibration, while blue elements denote the results derived from n = 50 independent stochastic simulations. In (a–c), observed data are smoothed using a 7-day rolling average. Blue solid lines represent the simulation medians, and the shaded areas represent the error bands defined by the minimum and maximum range across the n = 50 simulations. In (d) individual simulation runs are displayed as semi-transparent dots, overlaid with dual-layer error bars showing the median (circles), 10th–90th percentiles (thick lines), and full range (thin lines). Text labels above the data points indicate the odds ratios (OR), denoting the median calibrated relative susceptibility for each age group. Source data are provided as a Source Data file.

The calibrated baseline model demonstrated an acceptable fit to observed data across all target metrics (Fig. 2) and yielded consistent results under alternative data subsets and target weighting choices (Supplementary Results section 1.2 and 1.3), supporting the robustness of the model fitting. Parameter estimates revealed season-specific variation in key transmission drivers (Supplementary Table 1 and Supplementary Results section 1.1). Estimated numbers of initial infections were highest in seasons 1 (pandemic) and 4, consistent with their elevated overall incidence. Across all seasons, adults aged ≥65 years exhibited consistently higher susceptibility than other age groups, with odds ratios ranging from 1.4 to 3.1 compared to younger individuals. In addition, susceptibility among individuals aged 0–24 years was highest in season 1 compared to the same age group in other seasons, consistent with the substantially elevated attack rate observed in this age group during that season. The estimated adherence to stay-home behavior upon seeking healthcare was highest in Season 1 (5.0% of symptomatic individuals staying home due to illness), which was higher than in other seasons (1.8–3.8%).

Age-targeted vaccination

Across six seasons, vaccinating children under 12 consistently resulted in the largest reductions in population attack rate, with absolute reductions ranging from 0.58 to 2.60 percentage points and relative reductions from 6.8% to 8.5% per 100,000 vaccinated individuals (Fig. 3 and Supplementary Fig. S3). Targeting individuals under 18 showed moderate effectiveness (absolute reductions: 0.38 to 1.78 percentage points; relative reductions: 5.3–6.9% per 100,000 vaccinated), while vaccination of those aged ≥ 65 yielded smaller reductions (absolute reductions: 0.14 to 1.21 percentage points; relative reductions: 0.8– 5.5% per 100,000 vaccinated). Universal vaccination was the least efficient strategy, yielding only modest reductions (absolute reductions: 0.03 to 0.39 percentage points; relative reductions: 2.2% to 2.6% per 100,000 vaccinated), with marginal effects declining substantially as coverage increase (Supplementary Results section 2.1).

Fig. 3. Impact of age-targeted vaccination strategies on attack rate.

Each color represents a distinct age-targeted vaccination strategy. The x-axis denotes the number of individuals vaccinated under each strategy across varying coverage levels. For each strategy, five vaccination expansion levels are shown, representing 10–50% increases in coverage at 10% increments. The points indicate the median values derived from n = 50 independent stochastic simulations, and the solid lines represent the corresponding linear regression fits summarizing the simulation trends. The vertical error bars represent the 10th and 90th percentiles calculated across these n = 50 simulations. Source data are provided as a Source Data file.

Further analysis showed that targeting vaccination to children under 12 not only substantially reduced attack rates within this group (absolute reductions: 1.01 to 6.10 percentage points; relative reductions: 7.1–9.3%, per 100,000 vaccinated), but also conferred indirect protection to adolescents ( < 18 years: absolute reductions 0.78 to 4.51 percentage points; relative reductions: 6.8–9.1% per 100,000 vaccinated) and older adults ( ≥ 65 years: absolute reductions 0.52–2.88 percentage points; relative reductions 6.4–8.4% per 100,000 vaccinated) (Supplementary Fig. S4). Targeting individuals under 18 also benefited older adults, though to a lesser extent (absolute reductions: 0.28–2.02 percentage points; relative reductions: 5.0–6.9% per 100,000 vaccinated). In contrast, prioritizing vaccination in adults aged ≥65 had limited indirect impact on younger age groups, with reductions among children < 18 observed in five of six seasons (absolute reductions: 0.10 to 0.77 percentage points; relative reductions: 0.8%–4.3% per 100,000 vaccinated) and no significant effect in season 1.

Differences in indirect effects reflected the directionality of age-specific transmission (Supplementary Results section 2.2). At baseline, 19–43% of infections in older adults ( ≥ 65 years) originated from individuals aged 0–24 years across seasons, while only 2–6% of infections in the 0–24 age group originated from older adults. In the +30% coverage scenario, targeting children ( ~ 0.8–1.0 million vaccinated) resulted in greater reductions in infections among adults aged 25–64 than targeting older adults ( ~ 0.9–1.2 million vaccinated), despite requiring fewer vaccine doses.

Non-pharmaceutical interventions (NPIs)

Increasing the daily probability of adherence to staying home when sick by 10–50% (resulting in 6–30% of symptomatic cases staying home) reduced the attack rate by 3–46% compared to the baseline across all six seasons. In contrast, increasing population mask usage by 10–50% (equivalent to 20–60% of the population using masks) achieved an 8–63% reduction in attack rate (Fig. 4a).

Fig. 4. Impact of non-pharmaceutical interventions on attack rate.

a Effect of varying coverage levels of staying home when sick and mask use on the overall attack rate. Coverage for staying home refers to the proportion of symptomatic individuals adhering to staying home; coverage for mask use refers to the proportion of the total population wearing masks. Points represent the median attack rates derived from n = 50 independent stochastic simulations for each parameter combination. b Comparative effectiveness of staying home when sick and mask use under different probabilities of asymptomatic infection. Points indicate the median attack rates, and the vertical error bars represent the 10th and 90th percentiles calculated across the n = 50 simulations. Source data are provided as a Source Data file.

We estimated that population-wide masking (40% coverage, Mask + 30% scenario) reduces influenza transmission as effectively as 20–30% of symptomatic individuals staying home (Stay-home + 50% scenario). Across six seasons, both strategies achieved similar overall reductions in attack rates (18–43% for masking vs. 17–46% for staying home), though their relative effectiveness varied slightly by season (Supplementary Table 7). However, the effect of masking is sensitive to assumptions about mask efficacy and adherence: for example, if adherence drops to 25%, a higher coverage of 60% is required to achieve a similar level of protection (Supplementary Results section 6). Their relative effectiveness also varied with asymptomatic infection proportions. While mask effectiveness remained stable, the effectiveness of staying home declined as the asymptomatic proportion increased. Under the Stay-home + 50% scenario, increasing the asymptomatic infection probability from 20% (baseline) to 60% resulted in an absolute increase of 0.4–3.3 percentage points in the overall attack rate across seasons. (Fig. 4b).

Intervention effectiveness was sensitive to implementation timing, with staying home when sick more affected by delays than mask use (Supplementary Fig. S5). Higher coverage generally preserved effectiveness under short delays, but as delays increased, the difference between coverage levels narrowed. In high-transmission settings (e.g., Season 1), the median attack rate did not always increase with longer delays, possibly due to stochastic variation under low coverage conditions (Supplementary Results section 11).

Combined NPIs under low vaccine performance

In seasons with low vaccine coverage (baseline) or low vaccine effectiveness (i.e., mismatch seasons), combinations of NPIs were essential for reducing transmission. Figure 5 shows the attack rates under varying levels of combined NPIs across six influenza seasons, simulated under each season’s baseline vaccine coverage. Compared to the baseline scenario, increasing both NPIs by 30% under these low-coverage conditions led to relative reductions in median attack rates of 61, 45, 25, 60, 55, and 48% in Seasons 1 through 6, respectively. Notably, in mismatch seasons (Seasons 1 and 4), scaling both interventions from 10– 50% compliance resulted in reductions of 22–84% and 27–79%, respectively, compared to baseline. A statistically significant interaction indicating diminishing returns was observed between mask use and stay-home after adjusting for season effects (P < 0.001), though the effect size was negligible (β = ${8.3\times 10}^{-4}$; all variables were expressed in percentage points).

Fig. 5. Impact of combined non-pharmaceutical intervention strategies under baseline vaccination coverage.

Each heatmap cell denotes the median overall attack rate derived from n = 50 independent stochastic simulations across six influenza seasons; color gradients from red to blue represent higher to lower attack rates. Simulations assume baseline vaccination coverage, with seasonal age-specific vaccination rates (Vac %) detailed in the accompanying tables. Increases in staying home reflect a higher probability of adherence to staying home when sick.

School closure and targeted strategies for school-aged children

In seasons without overlap with summer holidays (seasons 3, 4 and 5), where school transmission was continuous without scheduled interruptions, we evaluated three school-based interventions: student vaccination, student stay-home-when-sick, and temporary school closures (Figs. 6a, b). When coverage increased from 10% to 50% for each intervention, student vaccination consistently achieved the greatest reductions in both student attack rates (53–85%) and overall population attack rates (47–77%). Staying home when sick among symptomatic students showed variable effectiveness, reducing student rates by 23–56% and overall rates by 15–46%. School closures had the smallest impact, with student reductions of 18–33% and overall reductions of 21–26%.

Fig. 6. Impact of interventions targeting school-age children.

a Effectiveness of three interventions on the student attack rate. b Effectiveness of three interventions on the overall population attack rate. For both (a, b), points represent outcomes from n = 50 independent stochastic simulations, and lines correspond to linear regression fits summarizing the simulation trends. c Combined effect of school vaccination and general non-pharmaceutical interventions (NPIs) on the overall population attack rate. d Combined effect of school closure and general NPIs on the overall population attack rate. General NPIs include both mask use and staying home when sick. For both heatmaps, each cell represents the median overall attack rate derived from the n = 50 independent stochastic simulations under each parameter combination; color gradients from red to blue represent higher to lower attack rates.

Combined effects of school-based interventions and population NPIs

We further evaluated the interaction between school-based interventions (student vaccination and school closures) and general population-level NPIs (mask use and staying home when sick) across Seasons 3, 4, and 5 (Fig. 6c, d). Student vaccination consistently provided additional benefit when layered on top of general NPIs. In contrast, school closures at low ( + 10%) and moderate ( + 30%) levels yielded only modest absolute reductions in median attack rates (0.0–0.8% and 0.1–2.3%, respectively). Significant interaction effects between general NPIs and both student vaccination (β = ${1.5\times 10}^{-3}$, P < 0.001) and school closures (β = ${7.1\times 10}^{-4}$, P < 0.001) indicate diminishing returns when combined (Supplementary Result section 3).

Sensitivity analyses showed that the key conclusions remained robust under joint variation of multiple parameters (Supplementary Results section 7–10). The relative effectiveness of interventions and the overall patterns of attack rate reduction were broadly consistent across both lower-bound and upper-bound parameter settings.

Discussion

We calibrated the model using infection time series from surveillance and serological data, and incorporated school absenteeism to inform school-based intervention. By simulating six influenza seasons in Hong Kong (2009–2013) across varied virus subtypes and vaccine matches, our model quantifies the differential impact of vaccination and non-pharmaceutical interventions. Child vaccination consistently reduced transmission, underscoring children’s pivotal role as infection amplifiers in dense urban settings and supporting targeted immunization policies. Among non-pharmaceutical measures, mask use showed robust and stable effectiveness comparable to moderate levels of staying home when sick, highlighting its value as a reliable control strategy. Importantly, during vaccine-mismatched seasons, combined interventions were crucial to maintaining epidemic control. Furthermore, school-based vaccination demonstrated superior effectiveness and sustainability compared to reactive closure strategies.

Vaccination strategies targeting children consistently outperformed alternatives, reflecting both strong direct protection and substantial indirect benefits at the population level. This finding is well-supported by modeling studies from the US and UK, and notably by a community-based trial in Hong Kong where increasing child coverage halved child attack rates while also reducing adult rates, demonstrating important indirect protection^26–28. Children are highly exposed in school settings and typically exhibit stronger immune responses to influenza vaccines than adults, leading to higher effectiveness²⁹. Vaccinating this group also reduces onward transmission, as children play a central role in community spread due to their high contact rates³⁰ and elevated transmissibility³¹, These findings support the expansion of Hong Kong’s Seasonal Influenza Vaccination (SIV) School Outreach Program to include adolescents under 18, which proved more efficient than universal or elderly-targeted strategies. As the benefits of child vaccination are largely indirect, uptake may remain suboptimal without targeted incentives³².

The lower per-dose efficiency of universal vaccination reflects two reinforcing mechanisms. First, in a nonlinear transmission model, the attack rate reductions from vaccinating different age groups are not additive: vaccinating one group alters the transmission landscape and thus the marginal benefit of vaccinating others. As a result, universal vaccination efficiency cannot be expressed as a weighted average of age-specific efficiencies and may fall outside the range defined by the most and least efficient targeted strategies. Second, universal vaccination progressively allocates doses to individuals with limited transmission potential, causing its per-dose efficiency to decline more steeply with increasing coverage than any targeted strategy (Supplementary Figs. S13, S14).

Beyond vaccination, other school-based interventions provide moderate mitigation. Encouraging symptomatic students to stay home reduces transmission meaningfully, consistent with CDC recommendations showing modest reductions under partial compliance³³, emphasizing the importance of promoting voluntary isolation. In contrast, short-term reactive school closures produced limited effects in our simulations, aligning with systematic reviews showing that brief closures achieve only modest reductions³⁴, unless repeated or extended under high compliance^35,36. Given their limited epidemiological benefit and considerable social and economic costs, school closures should be carefully weighed against more targeted and sustainable interventions.

Mask use provides population-level control that does not rely on symptom recognition or individual adherence decisions. Even widespread but not universal use can meaningfully reduce transmission through network effects, where preventing early transmission events disproportionately constrains total outbreak size³⁷. Laboratory and meta-analytic studies support substantial per-contact efficacy of surgical or cloth masks^12,38. Compared to stay-home policies, masks maintain more consistent effectiveness across seasons because they protect regardless of symptom awareness. However, effectiveness still varies with baseline transmissibility and intervention timing^37,39.

Our simulations indicate that voluntary stay-home policies among symptomatic individuals can achieve meaningful transmission reductions, even with modest voluntary levels. While baseline compliance is typically low due to mild symptoms and limited paid sick leave⁴⁰, increasing participation to feasible levels produced notable mitigation, consistent with workplace studies showing substantial infection reductions with partial sick leave uptake⁴¹, and community simulations demonstrating comparable benefits^42,43. However, financial disincentives such as income loss⁴⁴ often discourage adherence, especially in the absence of supportive policies. The widespread adoption of remote work arrangements following the COVID-19 pandemic may have increased the feasibility of staying home when sick, particularly for office workers. However, when economic constraints prevent staying home, public health authorities may need to recommend less effective but more accessible alternatives, such as mask use.

Unlike mask use, which provides population-wide protection regardless of infection awareness, staying home when sick depends on individuals recognizing symptoms and voluntarily avoiding contact with others. Its effectiveness is therefore influenced by the timeliness of symptom detection and the consistency of individual adherence. The presence of asymptomatic infections, which are common in influenza and vary in estimated prevalence across studies⁴⁵, further limits the effectiveness of staying home when sick. Without complementary strategies such as contact tracing, this strategy remains modest in effect and operationally challenging to implement.

Vaccine mismatch seasons, common in influenza epidemics^9,46, highlight the need for early and sustained non-pharmaceutical interventions to control transmission effectively. This aligns with previous studies showing that vaccination alone is insufficient under high-transmission conditions and that multiple interventions are needed to suppress transmission⁴⁷. However, our assumption of constant adherence likely overestimates real-world impact, as behavioral responses often weaken over time^48,49. Moreover, interactions between interventions—such as reduced NPI adherence after vaccination or lower vaccine uptake when NPIs are widespread—may influence overall impact⁵⁰. Future models should account for these behavioral dynamics to better inform integrated strategies.

The feasibility of implementing key mitigation strategies has improved in recent years. Seasonal influenza vaccination coverage in Hong Kong has increased steadily due to long-standing government efforts. For instance, in the 2024/25 season, coverage reached 73.8% among children aged 6 to under 12, and over 50% among adults aged 65 or above⁵¹. These levels indicate that expanding vaccine uptake is not only feasible but is actively being implemented in practice. NPIs have also become more acceptable and actionable in the post-COVID context. Public awareness of respiratory hygiene, mask-wearing⁵², and self-isolation when symptomatic has increased substantially. In parallel, the experience of the pandemic has raised awareness about the potential benefits of flexible work and school arrangements (e.g., work-from-home policies, hybrid learning) for enabling individuals to stay home when sick, though widespread implementation remains an ongoing challenge⁵³. Together, these developments suggest that the implementation of NPIs may be more practical than during the pre-COVID period. While our model was calibrated using pre-COVID data, the core transmission mechanisms remain valid. Nevertheless, future research should consider updating behavioral assumptions using post-COVID data to reassess intervention impacts under evolving social norms and contact patterns.

Based on our findings, we propose a signal-responsive policy framework that links early-season surveillance indicators to adaptive interventions (Fig. 7). Routine vaccination of children and older adults serves as the foundation, aligned with Hong Kong’s expanded free vaccination program. Additional NPIs, such as mask use and stay-home-when-sick policies, can be activated when early signals suggest vaccine mismatch or low vaccine coverage. Furthermore, when there is elevated asymptomatic transmission, non-symptom-based measures should be strengthened. As NPIs are sensitive to implementation delays, timely deployment is critical. Delayed action may require higher intensity or broader coverage to remain effective. If transmission continues, especially among children, school-based measures should be considered. Within schools, a tiered approach is recommended: begin with school-based vaccination, enforce stay-home-when-sick policies, and consider temporary closures only if transmission remains high despite earlier interventions.

Fig. 7. Surveillance-informed response framework.

This conceptual model maps adaptive response strategies to time-varying epidemic status and surveillance indicators. The background gray curve and shaded band illustrate a representative epidemic trajectory using Season 1 baseline data, where the solid line indicates the median daily new infections and the shaded area represents the minimum-to-maximum range across n = 50 independent stochastic simulations.

This study offers several methodological strengths. First, analyzing six influenza seasons under varying epidemiological conditions enhanced the generalizability of our findings. Second, calibration using serology-based attack rates, rather than clinical surveillance data alone, enabled more accurate estimation of total infections, including asymptomatic cases. While some prior studies incorporated serological data^54,55, these focused exclusively on the 2009 H1N1 pandemic and used serology only to estimate seasonal attack rates without integrating surveillance data, lacking temporal resolution and sometimes using data from different seasons or subtypes. In contrast, we utilized contemporaneous, population-specific serological data integrated with surveillance systems to reconstruct age-specific epidemic curves, capturing both reported and unreported infections with daily resolution. Third, incorporating school absenteeism data enabled us to model illness-related behaviors in school-aged children, a key driver of influenza transmission, and to establish a more realistic behavioral baseline often omitted in models. This comprehensive approach improved model realism and strengthened the reliability of intervention impact assessments.

Several limitations should be noted. First, our analyses focused on infections and did not capture clinical severity or mortality, limiting its ability to reflect total disease burden. Second, antiviral treatment was not considered in the analyses due to low uptake in Hong Kong. Third, we used a population scaling approach in the model, which may underestimate the uncertainty of epidemic trajectories by reducing inter-agent heterogeneity (Supplementary Results Section 4). Fourth, the model simplified population and behavioral heterogeneity. Some parameters, such as the probability of symptomatic infection, were not age-specific, potentially underestimating differences across demographic groups. In addition, behavioral factors such as mask use and health-seeking were assumed to be constant over time, which may not reflect real-world changes in response to epidemic dynamics or public health messaging. Fifth, the effectiveness of interventions was simplified. While the model used a binary classification of vaccine match, sensitivity analyses across a range of vaccine effectiveness values yielded consistent results (Supplementary Results Section 5), supporting the robustness of our conclusions. However, this approach does not capture intra-seasonal strain variation or subtype dynamics. Masking was implemented as a simplified reduction in per-contact transmission probability. While this facilitates comparison across scenarios, it may not fully capture the non-linear effects of repeated exposures or heterogeneous contact patterns. Accordingly, the estimated impact should be interpreted with caution and understood as conditional on these assumptions. Lastly, the model did not capture behavioral interactions between interventions, such as reduced NPI adherence following vaccination.

In summary, this study used a multi-season, age-structured model calibrated with serological, surveillance and school absenteeism data to evaluate vaccination and NPIs for influenza control in Hong Kong. By integrating diverse data sources and capturing behavioral and seasonal variability, the model provides a robust tool for evaluating targeted strategies. The findings support child-targeted vaccination and emphasize the complementary role of NPIs, particularly during vaccine-mismatched seasons. School-based interventions further highlight the advantages of proactive measures like student vaccination over reactive strategies such as closures. This framework offers actionable insights for influenza control and broader respiratory preparedness.

Methods

Ethics

Institutional ethical approval and informed consent were not required for this study, as the research involved exclusively secondary analyses of de-identified, aggregated, or publicly available data. The individual-level primary data collection was outside the scope of this work, and the dataset contained no personally identifiable information.

Data sources

Data for this study were obtained to capture a comprehensive picture of influenza activity over six seasons in Hong Kong (2009–2013) (Table 1). Multiple, high-quality sources provided the basis for the diverse datasets used in this analysis.

Demographic and social structure data, including age-stratified population figures, employment statistics, enrollment numbers, and school capacity records, were sourced from governmental agencies and public institutions. These datasets offered detailed insights into the population structure and social mixing patterns in Hong Kong to generate the contact matrix.

Influenza activity was monitored through surveillance systems that recorded the percentage of outpatient visits attributed to influenza-like illness (ILI) alongside the proportion of laboratory-confirmed influenza cases from public health laboratories. The weekly influenza activity proxy was derived by multiplying these two indicators.

Serology data were collected from two community-based randomized controlled trials (RCTs) for evaluating direct and indirect benefits of influenza vaccination^56,57. In the RCTs conducted in 2008/09 and 2009/10, 119 and 796 households were recruited. Serum specimens were collected at the start of the study, and after 6 and 12 months from all participants. In the subsequent observational follow-up of the same cohort participants from late 2010 to late 2013 without intervention⁵⁸, serum specimens were collected from all participants in each autumn (October to December), and also each spring (April to May). Receipt of influenza vaccine outside of the trial was recorded annually. Age-specific cumulative infection incidence estimates were obtained from Tsang et al. (2022)⁵⁹, who analyzed longitudinal serological data from household cohort studies in Hong Kong during 2009–2013. These estimates were derived using a Bayesian approach that reconstructs antibody dynamics from hemagglutination inhibition (HAI) titer measurements, accounting for antibody boosting, waning, measurement error, and the timing of serum collection. This method probabilistically identifies infections and captures cases that would be missed by traditional 4-fold rise criteria (see Tsang et al., 2022, for full methodological details). Age-stratified cumulative incidence estimates (for children ≤ 17 years, adults 18–50 years, and older adults ≥ 51 years) were available for six epidemic periods: three H1N1 and three H3N2 seasons between 2009 and 2013.

School absenteeism data were collected through a smartcard-based monitoring system covering 66 primary and 41 secondary schools across all 18 districts of Hong Kong, encompassing 75,052 students⁶⁰. This system tracked daily attendance patterns and class sizes, providing data on all-cause absenteeism. To estimate influenza-attributable absenteeism, we adjusted the all-cause absenteeism data using ILI consultation rates and specimen positivity rates from the established surveillance systems.

Crucially, the serological data and school absenteeism data utilized in this study were obtained as de-identified, aggregated secondary datasets. No individual-level demographic data (such as specific sex or gender) were accessible to the investigators, making sex- or gender-disaggregated stratification infeasible, and participant compensation not applicable to this study.

Intervention-related data, including effectiveness, baseline coverage, and implementation timing of various interventions, were obtained through a literature review and from official government sources (Supplementary Methods section 4, Supplementary Table 4 and 5).

Model details

Covasim was originally developed for SARS-CoV-2, hence, we refined the model to capture the transmission characteristics and epidemiology of influenza (Supplementary Methods section 1). It explicitly represents the progression of the disease through distinct states within the population. In the model, individuals transition from a susceptible state to exposed, then progress to either symptomatic or asymptomatic infection, with an 80% probability of developing symptoms, before ultimately recovering (Fig. 1).

To mirror the approximately 7 million inhabitants of Hong Kong, we constructed a synthetic population of about 70,000 agents using a scale-up factor of 100 to reduce complexity while maintaining accuracy²⁵. This population was designed to reflect Hong Kong’s demographic composition by incorporating comprehensive data, such as age distributions, employment statistics, and school enrollment figures. These data underpin the development of realistic contact networks that span households, schools, workplaces, and community settings (Supplementary Methods section 2.1 and Supplementary Table 2), capturing the heterogeneous nature of social interactions in an urban environment. Initial parameter values were sourced from existing literature and established assumptions.

The transmission model incorporates empirically-derived parameter values obtained through literature review and calibration to Hong Kong surveillance data. This includes age-specific susceptibility profiles, transmissibility factors, and disease progression timelines. Importantly, the model integrates actual NPI measures and documented vaccine coverage data from the study period. By incorporating real-world values for interventions such as staying home when sick and mask use, alongside empirical vaccination coverage across various age groups, the model accurately mirrors the public health strategies implemented during the observed influenza seasons. Detailed numerical assumptions and parameter values governing these processes are summarized in Supplementary Table 1.

Calibration

The model was calibrated using three types of observational data: influenza surveillance, serological data, and school absenteeism records (Supplementary Methods section 3). These informed three calibration targets: (1) cumulative infections per day, (2) daily new infections stratified by age group, and (3) influenza-related absences among students aged 6–18 years.

To reconstruct age-specific infection time series for six influenza seasons, we combined the weekly influenza activity proxy with age-specific cumulative incidence estimates derived from serological data using a likelihood-based method adapted from Tsang et al.⁵⁹. This approach relaxes the conventional 4-fold rise assumption and leverages the full distribution of antibody titers. The resulting cumulative incidence estimates were temporally distributed based on the normalized weekly influenza activity proxy curve, yielding daily infections by age group. These time series formed the basis for the first two calibration targets, with age weighting applied to the second. The third target was estimated by adjusting all-cause absenteeism data using ILI consultation and laboratory positivity rates, as detailed in the Data Sources section.

We estimated four parameters through calibration: the initial number of infections, the per-contact transmission probability, age-specific susceptibility, and the probability of staying home when symptomatic among individuals who seek healthcare. All other parameters were fixed to literature-based values to reduce overfitting and ensure model identifiability. A schematic overview of the calibration framework is provided in Supplementary Fig. S1.

We employed the Optuna 3.2.0 hyperparameter optimization framework in Python and conducted 40,000 simulation runs for each influenza season to ensure robust parameter estimation.

Intervention strategies

We systematically assessed age-targeted vaccination approaches, staying home when sick, community mask-wearing, and school-based interventions. Table 2 summarized the strategy specifications and parameter configurations employed in our primary analysis.

Table 2.

Intervention strategies

Intervention	Target	Contact layers	Intervention level	Efficacy	Baseline coverage	Scenarios
Vaccination	• < 12 y < 18 y ≥ 65 y Both < 18 y and ≥ 65 y Universal	All	Individual	Matched: 70% Mismatched: 30%	• 0–5 y: 7.5%–12.9% 6–11 y: 10.8%–18.4% 12–17 y: 5.1%–8.8% 18–39 y:2.7%–3.3% 40–61 y: 8.4%–9.8% ≥ 65 y: 28.1%–32.7%	Coverage +10% increments from baseline
Staying home when sick	Symptomatic cases	School, workplace, and community	Individual	80%	• Probability of symptomatic presentation: 80% Daily healthcare-seeking probability: ≤ 15: 18.1%, 16–54: 6.5%, and ≥ 55: 9.5% Daily stay-at-home adherence probability: calibrated	Daily adherence probability + 10% increments from baseline
Mask use	Universal	School, workplace, and community	Population (contact layer level)	25%	10%	Coverage + 10% increments from baseline
School closure	School-aged children (3–17 y)	School	Population (contact layer level)	100%	0%	Coverage + 10% increments from baseline; 14-day duration

We explored the impact of expanding influenza vaccination coverage across specific population segments, starting from documented baseline coverage levels (Supplementary Table 3). Five distinct targeting approaches were evaluated: (1) children under 12 years; (2) individuals under 18 years; (3) adults aged 65 and above; (4) combined targeting of both young ( < 18) and elderly ( ≥ 65) populations; (5) universal vaccination across all age groups. In addition, we simulated a school-based vaccination program specifically targeting children aged 3–17 years. Vaccine efficacy parameters reflected documented seasonal variation, with 70% efficacy during antigenically-matched seasons and 30% during mismatched seasons⁶¹. Immunity was assumed to be acquired following vaccination or natural infection (Supplementary Methods section 2.6). Natural infection conferred complete protection for the remainder of the same season, whereas vaccination provided partial protection, with breakthrough infections allowed and immunity waning at a rate of 14% per year⁵⁹.

In the baseline scenario, staying home when sick reflected existing behavior, where symptomatic individuals remained at home due to illness severity. Enhanced interventions represented increased work-from-home policies and higher public adherence to stay-at-home recommendations. This behavior was modeled using a probability function:

$$p_{\mathrm{sh}}\left(i\right)=p_{\mathrm{sym}}*\left[1-{\left(1-p_{\mathrm{hs}}\left(i\right)*p_{\mathrm{ad}}\right)}^{T_{\mathrm{rec}}-1}\right]$$ 1

where $p_{\mathrm{sym}}$ is the probability of symptomatic presentation, $p_{\mathrm{hs}}\left(i\right)$ is the age-specific daily probability of healthcare-seeking behavior among symptomatic individuals, $p_{\mathrm{ad}}$ is the daily probability of adherence to stay-at-home behavior following healthcare-seeking among symptomatic individuals, and $T_{\mathrm{rec}}$ is the duration from symptom onset to recovery in days. We assumed a one-day delay between symptom onset and initiation of stay-at-home behavior. Intervention scenarios simulated enhanced adherence by increasing $p_{\mathrm{ad}}$ relative to the baseline, which was calibrated to observed behavior.

In addition to population-wide measures, we simulated a targeted strategy focusing on school-aged children (aged 3–17), reflecting potential guidance encouraging symptomatic children to stay home until recovery. Staying home when sick reduced transmission in community, workplace, and school settings, while household transmission remained unchanged as infected individuals continued interactions with household members.

Mask-wearing was implemented at the contact layer level, modeled as a reduction in per-contact transmission probability across school, workplace, and community settings. The baseline scenario assumed 10% population coverage of masks and 25% per-contact effectiveness⁶². This corresponds to an average 2.5% reduction in transmission probability at the population level, assuming homogeneous mixing. No transmission reduction was applied within households, where mask use was considered impractical. Intervention scenarios progressively increased the proportion of mask users in the population.

School closures were modeled by reducing per-contact transmission within the school contact layer. Coverage levels corresponded to proportional reductions in transmission relative to baseline: 0% indicated no closure and 100% represented full closure. Seasons overlapping with the summer holiday period (July 15 to August 31) were excluded, as the holiday inherently reduces school-based transmission. For seasons without such overlap, we modeled 14-day reactive school closures¹³ triggered by elevated absenteeism rates among school-aged, defined as daily absenteeism exceeding 200 students.

Intervention timing

We assumed vaccination occurred prior to influenza season onset (Supplementary Methods section 4.5). Implementation of staying home when sick and mask use aligned with HK CHP’s announcements of the onset of influenza seasons (Supplementary Table 4). We assessed timing sensitivity by simulating delays in NPI implementation ranging from 1 to 5 weeks after season onset.

Comparative analysis framework

To optimize mitigation approaches, we implemented a layered analysis framework that progressively added interventions to baseline vaccination scenarios. This structured approach allowed for systematic assessment of the incremental benefit of each additional public health measure. Specifically, we assessed: (1) age-targeted vaccination strategies; (2) the comparative effectiveness of staying home when sick and mask use; (3) combined NPIs in vaccine-matched and vaccine-mismatched seasons; and (4) the necessity of school closures by comparing their effectiveness with other school-based interventions—including vaccination and staying home when sick among school-age children—given the substantial societal costs associated with school closures as a mitigation measure⁶³.

Sensitivity analysis

To examine the robustness of our findings under parameter uncertainty, we conducted a multi-way sensitivity analysis by jointly varying key epidemiological parameters to their respective lower and upper bounds (Supplementary Table 1). These parameters included: latent and infectious periods, age-specific transmissibility odds ratios, symptom probability, per-contact transmission weights across settings, daily contact rates, age-specific healthcare-seeking behavior, and the effectiveness of staying home when sick and mask use. Following parameter adjustment, we re-calibrated the model for each extreme scenario and repeated the main analyses using the re-calibrated models.

Statistics & reproducibility

No statistical method was used to predetermine sample size. To mitigate structural and seasonal operational biases, explicit data exclusion criteria were applied: (1) seasons overlapping with the summer holiday period (July 15 to August 31; Seasons 1, 2, and 6) were excluded from reactive school closure simulations, as scheduled institutional closures inherently eliminate school-based transmission pathways; (2) for Seasons 4–6, baseline calibration excluded early-season absenteeism data to avoid bias from abnormally high non-influenza-related attendance fluctuations. No other data were excluded. Simulation experiments were not randomized, and investigators were not blinded to allocation during experimental execution and outcome assessment.

To guarantee computational reproducibility and algorithmic transparency, the simulation framework was executed within Python version 3.8.6 (Python Software Foundation), deploying Covasim version 3.1.4 for disease progression modeling and Optuna version 3.2.0 for hyperparameter optimization. Model calibration comprised 40,000 optimization trials per influenza season to ensure robust parameter convergence. For each scenario, 50 independent stochastic simulations were performed, each using a distinct parameter set from the top 50 best-fitting calibration results. Stochastic projections are expressed as medians accompanied by 80% projection intervals (10th–90th percentiles)⁶⁴ to rigorously quantify parametric and stochastic uncertainty. Model robustness against parameter uncertainty was verified through multi-way sensitivity analyses, wherein key epidemiological parameters were jointly varied to their lower and upper boundaries, followed by full model re-calibration and re-analysis.

All statistical estimations and trend visualizations were executed in R software version 3.6.3 (R Foundation for Statistical Computing), with statistical significance tested at a two-sided P < 0.05. Specifically, linear regression models were applied to fit stochastic simulation outcomes across parameter gradients, characterizing and visualizing general trends. To assess the joint effectiveness of multi-layered interventions, linear mixed-effects models were formulated to test for interactions between combined measures, treating influenza seasons as a random effect to account for between-season heterogeneity.

Reporting summary

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

Author contributions

T.K.T., D.K.M.I., and B.J.C. designed the study. L.P. adapted the modeling framework and performed model simulation and calibration. L.P., Y.G., N.N.Y.T., X.H., and H.C.S. collected the data. L.P., B.J.C., D.K.M.I., and T.K.T. interpreted the results. L.P. wrote the first draft. All authors reviewed and approved the final manuscript.

Peer review

Peer review information

Nature Communications thanks Sen Pei and Ling Yin for their contribution to the peer review of this work. A peer review file is available.

Funding

This project was supported by the Theme-based Research Scheme (Project No. T11-712/19-N), General Research Fund (Project No. 17104220, 17106424 to T.K.T.) of the Research Grants Council of the Hong Kong SAR Government, the Health and Medical Research (HMRF) Commissioned Program for Influenza Research (INF-HKU-2), and HMRF Research Fellowship Scheme (Project No. 05190097 to T.K.T.) from Health Bureau of the Hong Kong SAR Government. B.J.C. is supported by an RGC Senior Research Fellowship (grant number: HKU SRFS2021-7S03) and the AIR@innoHK program of the Innovation and Technology Commission of the Hong Kong SAR Government.

Data availability

Source data for Figs. 2, 3, and 4 are provided with this paper. The demographic data, social structure data, and weekly influenza activity data used in this study are publicly available from open-access sources, as described in the Supplementary Methods. The serological data are from previously published cohorts and can be accessed via Tsang et al. (2022) [https://doi.org/10.1038/s41467-022-29310-8]. For the school absenteeism data, researchers interested in data access are encouraged to submit a formal request to the corresponding author (T.K.T.) or the relevant Institutional Review Board at the University of Hong Kong. To uphold ethical standards, protect participant privacy, and ensure appropriate data use, each request will undergo a case-by-case review and approval process. In addition, as the data include information collected from the participating school, access is subject to the school’s data ownership and governance requirements and may require approval from the relevant school authorities. Source data are provided in this paper.

Code availability

The customized simulation and analysis code developed in this study has been deposited in Zenodo under DOI: 10.5281/zenodo.20271157⁶⁵. The source code repository is also publicly accessible on GitHub at https://github.com/Liping-Peng/Influenza_ABM_HK.

Competing interests

B.J.C. reports honoraria from AstraZeneca, GlaxoSmithKline, Moderna, Roche and Sanofi Pasteur. The remaining authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-74857-5.