In the base case analysis, three different vaccination coverage strategies (S1, S2, and S3) were compared to strategy S0, regarding epidemiological outcomes (Table 3), economic outcomes (Table 4), and medico-economic outcomes (Table 5).

S1 vs. S0. Vaccinating 54% of the population aged 50–64 years against influenza (S1) significantly reduces GP consultations, hospitalizations, and mortality over an epidemic season compared to the S0 strategy. The model projects a decrease to 500,124 GP consultations (− 21.14%), with 116,385 fewer consultations in the “at risk” population. Hospitalizations are estimated to drop by 9486 (− 20.77%), including 3640 avoided within the “at risk” group. Additionally, 2990 deaths are prevented (− 23.47%) using the S1 strategy compared to S0.

These reductions in epidemiological metrics lead to significant savings for hospitalization and GP consultation costs, resulting in savings of €− 66,106,287 (97.98% of those savings come from hospitalization costs reduction). However, the model estimated an additional vaccination cost of €124,301,812 for S1. As a result, strategy S1 incurs an additional cost of €58,195,525 compared to S0.

These improvements in epidemiological metrics also entail an increase in QALY of the population over individuals’ lifetimes, with a total increase of 38,890 QALY. Thus, the S1 strategy, compared to S0, leads to an incremental cost-effectiveness ratio (ICER) of €1496/QALY. Strategy S1 can be considered cost-effective compared to S0, as its ICER falls below the National Institute for Health and Care Excellence (NICE)'s stated threshold for cost-effectiveness, set at £20,000/QALY (or €30,000/QALY). This threshold was chosen due to the lack of an officially established cost-effectiveness threshold for France.

Considering indirect costs, the total savings in scenario S1 amount to €− 314,308,377, resulting in a dominant ICER of €− 8082/QALY, which indicates that S1 would be a more cost-effective and cost-saving strategy compared to S0.

S2 vs. S0. S2 is a less optimistic vaccination coverage strategy than S1, with only 25.4% of “not at risk” individuals between 50 and 64 years old vaccinated instead of 54% for S1. Compared to S0, S2 leads to a simulated reduction of 287,615 GP consultations (− 12.16%), 5598 hospitalizations (− 12.26%), and 1735 deaths (− 13.62%). These reductions place the epidemiological impact of S2 at an intermediate level between S0 and S1.

These increases in healthcare figures result in €− 39,479,141 of savings regarding GP consultations and hospitalizations (98.09% of those savings come from hospitalization costs reduction). However, with €70,773,813 in additional vaccination costs for S2, the second scenario is estimated to cost €31,294,672 more than S0.

The ICER of S2 compared to S0 can thus be calculated and is estimated at €1391/QALY, which is considered cost-effective. When indirect costs are included, the total savings increase to €− 184,621,148, resulting in a dominant ICER €− 8205/QALY with both quality-of-life improvements and cost savings.

S3 vs. S0. S3 is a vaccination coverage strategy with only 25.4% of individuals between 50 and 64 years old vaccinated instead of 54% for S2. Simulated reductions between S3 and S0 include 159,442 fewer GP consultations (− 6.74%), 2894 fewer hospitalizations (− 6.34%), and 951 fewer deaths (− 7.47%). This reflects a smaller decrease in healthcare outcomes compared to the S2 versus S0 scenario. These healthcare reductions result in €− 20,045,707 of savings related to GP consultations and hospitalizations (97.93% of those savings come from hospitalization costs reduction). However, with €38,180,810 in additional vaccination costs for S3, the strategy S3 is projected to cost €18,135,104 more than S0.

The ICER of S3 compared to S0 is estimated at €1464/QALY, deeming it cost-effective. When indirect costs are factored in, total savings rise to €− 102,169,629, leading to a dominant ICER of €− 8249/QALY with both quality-of-life improvements and cost savings.

S WHO is based on the vaccinal strategy goal of the World Health Organization with a vaccination coverage of 75% for people older than 65 years old and for “at risk” population and 5% for under 65 years old “not at risk” people. The simulated reductions between S WHO and S0 include 580,746 fewer GP consultations (− 24.55%), 12,388 fewer hospitalizations (− 27.13%), and 4302 fewer deaths (− 33.76%), showing an important decrease in the effects of influenza epidemic on healthcare.

These reductions result in €− 84,594,958 of savings on GPs consultations and hospitalizations (98.05% of those savings come from hospitalization costs reduction). However, with € 171,470,317 in additional vaccination costs, S WHO is projected to cost € 86,875,360 more than S0. The ICER of S WHO compared to S0 is estimated at €1724/QALY, which is considered cost-effective. Including indirect costs, total savings increased to €− 317,730,424, resulting in a dominant ICER of €− 6305/QALY with both improved quality of life and cost savings.

The simulated reductions between S4 and S WHO include − 494,127 fewer GP consultations (− 27.69%), 8892 fewer hospitalizations (− 26.72%), and 2583 fewer deaths (− 30.60%). These healthcare reductions result in €− 144,968,934 in savings on GPs consultations and hospitalizations (97.88% of those saving come from hospitalization costs reduction). However, with €302,482,903 in additional vaccination costs for S4, the strategy S4 is projected to cost € 70,638,609 more than S WHO. The ICER of S4 compared to S WHO is estimated to be dominant. When indirect costs are factored in, total savings rise to €− 285,282,361, leading to a dominant ICER of €− 7945/QALY with both quality of life improvements and cost savings.

Figure 2 allows for an understanding of the domination relationships between each scenario, and the frontier of efficiency, presenting the incremental individual QALY obtained regarding the investment needed to achieve it.

Strategies domination graph. QALY quality-adjusted life years

The model's validity was ensured by deterministic sensitivity analysis (DSA) and probabilistic sensitivity analysis (PSA) of the strategy S1 compared to the strategy S0 to emphasize the range of uncertainty of the most effective strategy.

DSA is a method used to assess the robustness of model results by systematically varying key input parameters within a plausible range to observe their impact on the outcomes. This plausible range is either given by literature as a confidence interval or is supposed to be plus or minus 20% of the used value of the parameter. In this approach, one or more parameters are adjusted while keeping all other inputs constant, allowing for the identification of which variables have the most significant influence on the model’s results.

The DSA revealed that the vaccine administration cost is the principal factor influencing ICER. A tornado plot summarizing the 10 most influential parameters for ICER presented in Fig. 3 reveals that a 20% reduction in vaccine administration costs results in an ICER of €1195/QALY which is still positive. A 20% increase leads to an ICER of €1797/QALY which is still beneath the usually accepted cost-effectiveness threshold of €30,000/QALY. Being respectively the lowest and the highest ICERs of the DSA, these ICERs confirm the robustness of the cost-effectiveness conclusion for S1 compared to S0.

Deterministic sensibility analysis (DSA) tornado plot of the 10 most influential parameters for the ICER of the comparison of S1 and S0. ICER incremental cost-effectiveness ratio, QALY quality-adjusted life years

PSA is a technique used to evaluate the uncertainty in model outcomes by simultaneously varying multiple input parameters based on predefined probability distributions. PSA uses random sampling (typically through Monte Carlo simulations), 1000 times in this case, to account for the variability and uncertainty of all key parameters.

Therefore, a PSA was also conducted, and the scatter plots on the cost-effectiveness plane are presented in Fig. 4. Across 1000 simulations, the incremental costs and QALYs in the S1 versus S0 comparison are consistently positive, with all points falling below the cost-effectiveness threshold (set at €30,000/QALY), confirming the robustness of the cost-effectiveness. The probabilistic means of the simulations align closely with the incremental costs and quality of life of S1 compared to S0, further validating the reliability of the model's parameters despite uncertainty.

Probabilistic sensitivity analysis (PSA) scatter plot of incremental costs and QALYs entailed by S1 strategy and S0 strategy comparison over 1000 simulations. QALY quality-adjusted life years