We obtained 221 articles from a 2024 systematic review by Sbarra et al. that summarised the scope and bias in population-level measles serosurveys [6]. Surveys that did not provide information on the age distribution of the sampled population (n = 16) were excluded. We also excluded survey data from non-representative populations, such as immunocompromised patients, pre-term babies, and refugees or border populations (n = 21). Based on the bias assessment in the previous review [6], we further excluded surveys having a critical bias in the validity of the tools used to measure serology (n = 19). We did not exclude serosurveys that were rated lower quality because they had insufficient information when reporting serological results, because a standard reporting style was not widely used, especially in early studies, and because reporting completeness would not necessarily reflect the implementation quality of serosurveys.

From the 165 included articles, a total of 172 unique studies were defined with a unique combination of country, survey year, and first author (Table A in S1 Appendix). We extracted 13 unique studies from 6 articles, including survey data for multiple years or multiple countries. Where only the publication years were available, we approximated the survey years using the average duration between the survey and publication years in studies with complete information (3.7 years). In mother-newborn studies examining both the samples from mother-newborn pairs, we extracted the data only from mothers. Most such studies reported a high correlation in the antibody concentration between mother and newborn. The age-specific seroprevalence estimates were derived from surveys conducted between 1963 and 2019 in 57 LMICs, with the majority found in China, India, Türkiye, and Brazil (Fig A in S1 Appendix). Most of the included studies (n = 132, 76.7%) consisted of seroprevalence estimates across multiple age groups, and only a small proportion did not cover children (n = 21, 12.2%).

Dynamic Measles Immunization Calculation Engine (DynaMICE) is a compartmental model developed to capture measles transmission and assess the health impact of vaccination strategies at the country level. The model consists of four epidemiological states – maternally immune, susceptible, infectious, and recovered (Fig B in S1 Appendix), further stratified by the doses of measles-containing vaccines (MCV) received. DynaMICE is incorporated with fine-scale age structure, including 156 weekly age groups for children aged under 3 years old and 98 yearly age groups for those aged between 3 and 100 years old. In addition, modelling the force of measles infection takes into account annual seasonality via a sine function, pathogen transmissibility via R₀, and age-dependent mixing pattern via a contact matrix. We assumed the incubation period for measles to be 14 days and immunity following infection to be lifelong [10]. The proportion of newborns with maternal immunity was directly informed by the proportion of immune adults at child-bearing age (18–35 years old, ‘recovered’ compartments). We derived country-specific demographics from the United Nations World Population Prospects [11]. Country-specific synthetic contact matrices were obtained from Prem et al. [12] and modified to match the age structure of DynaMICE.

In modelling measles vaccination in DynaMICE, we applied country-specific vaccination schedules and coverage reported in the World Health Organization (WHO) Immunization Data portal [1]. Routine MCV1 and MCV2 doses were provided at the country-specific recommended age, and supplementary immunisation activities were implemented as one-off campaigns in the targeted age groups in the middle of the calendar year. We assumed vaccine effectiveness for MCV1 to vary linearly by age [13], two-dose vaccine protection to be capped at 98% [14], and no further protection from three or more MCV doses. Details of model structure, equations, parameters, and key assumptions have been included in the previous publication [8].

We fitted DynaMICE to each unique set of age-specific seroprevalence data per country-time period using Markov Chain Monte Carlo (MCMC) with component-wise Metropolis algorithm and random order for updating parameters in each blocked iteration [15]. Four MCMC chains for each study were conducted with starting parameters randomly drawn from their prior distributions. Three parameters―R₀, duration of maternal immunity protection, and vaccine effectiveness for the first MCV dose―were fitted, and they were assumed to be constant over time within the same serostudy. We selected less informative prior parameter distributions to cover a variety of settings for the 172 included serostudies (Table 1). We extracted prior distributions for R₀ and vaccine effectiveness from the systematic reviews [4,13] that gathered all the available evidence, and for the duration of maternal immunity, we used information from a longitudinal study with multiple follow-ups [16]. For 69 serosurveys conducted prior to country-specific MCV introduction, we removed the parameter for vaccine effectiveness and fitted the seroprevalence data with a two-parameter model. We constructed the likelihood by assuming the seroprevalence in each age group to be independently binomially distributed. We conducted diagnostic checks for convergence of MCMC chains and goodness-of-fit, with a targeting effective sample size above 200. We obtained 500 posterior samples for each study and calculated the medians and 95% credible intervals (CrI) of fitted parameters.

In our model-based outputs, we added up the non-susceptible populations ― maternally immune, infectious, and recovered sub-populations (compartments) [8] ― to calculate the seroprevalence in the corresponding age groups and calendar years. We included all the non-susceptible states because IgG antibodies, as the detection target in serosurveys, cannot distinguish between maternally acquired, infection-acquired and vaccine-induced immunity. Models were first simulated using the country-specific demographics in 1980 [11] and assumed no implementation of vaccination until they reached equilibrium. From 1980 to the survey year, we applied annual inputs of demographics and MCV coverage estimates [1] (Fig C in S1 Appendix). For serosurveys conducted before 1980, we extracted the model estimates in 1980, considering that seroprevalence was likely similar during earlier years, given low coverage of vaccination and other control measures for measles.

Measles R₀ is influenced by demographic, socioeconomic, and environmental factors, which change contact behaviours and transmission risk per contact in the population [4]. Although the DynaMICE model has accounted for country-specific age structure and age-dependent contact patterns, other factors could further contribute to the temporal and geographical variation in measles R₀. In addition, the survey quality and available details of seroprevalence data also affect the estimation of R₀ through fitting to seroprevalence data. To understand these dependencies, we evaluated the association between R₀ estimates and different study features, including survey period, age of the survey population, number of age-specific data points, and potential methodological biases. We used the bias assessment outcomes in Sbarra et al. [6], which evaluated the processes of sample selection, assay protocol, handling of equivocal results, and other information on serology testing methodology presented in the original serostudies under systematic, pre-defined algorithms. Serostudies were categorised into low, moderate, severe, and critical levels of biases in sampling, measurement and reporting serology. Unweighted bootstrapping was used to pool R₀ estimates and compare their distributions across the selected study features. For each selected feature, we filtered a subset of serostudies, and from their posterior samples, we randomly drew 10,000 bootstrapped samples with replacement.

We assessed the association of median R₀ for each study with average household size [17], population density [11], and Human Development Index (HDI) [18]. HDI is a country-specific and time-dependent summary measure combining the dimensions of health and longevity, education, and living standard. When these data were missing at specific survey years, we performed linear interpolation for household size and for HDI and population density, we used the estimate at the closest year on a country basis.

Using the posterior parameters of R₀, duration of maternal immunity, and vaccine effectiveness, we estimated the annual numbers of measles cases during the survey year and the two years before and after. We calculated the mean annual cases over the five years to reduce the influence of year-to-year fluctuations in the time series. We compared the model-based case estimates with the WHO country-specific reported cases [19] to assess their consistency in measuring measles burden and the potential issue of underreporting. We also compared our model-based estimates with measles incidence estimates from the Global Burden of Disease (GBD) Study 2021 [20], as it is a key publicly available resource for health decision makers.

We investigated the goodness-of-fit of the two-parameter and three-parameter models by calculating the root mean square error (RMSE) between the observed seroprevalence data and median posterior predictions. As the number of age data points is different in each serostudy, the RMSE metric enables comparison across studies by averaging the total error size. To assess how model fit affects the estimation of R₀, we ranked the RMSE and conducted a sensitivity analysis on the pooled R₀ results after removing 20% of the studies with the highest error size.

We conducted MCMC diagnostics and presented parameter trace plots, prior and posterior parameter distributions, pairwise parameter correlations, effective sample sizes, and Gelman-Rubin statistics in Figs D–G in S1 Appendix. We obtained 500 sets of posterior parameters from the converged MCMC chains. The posterior model estimates of age-specific seroprevalence show a good fit using the RMSE measure (Fig H in S1 Appendix), with two-thirds of the studies having an average difference less than 10% between the model results and observed data (S1 Fig). There was a positive correlation between median R₀ and vaccine effectiveness estimates (Spearman’s correlation coefficient (R)=0.3007, p-value (p)=0.0020). However, the correlation became weaker after excluding studies with a severe or critical bias in study population selection, serological measurement and result reporting (Fig I in S1 Appendix, R = 0.2558, p = 0.0485). No significant correlation between R₀ and duration of maternal immunity was found (R = 0.0122, p = 0.8739).

Fig 1 presents the median and 95% CrIs of the R₀ posterior distributions obtained from fitting the DynaMICE model to age-specific seroprevalence data in 172 individual studies. We observed a right skewed distribution of R₀ estimates, ranging widely across studies from 0.93 (95% CrI: 0.70–1.00) to 147 (95%CrI: 76.5–208). Only 12.8% (n = 22) of the median estimates were in the commonly cited range of 12–18 [3], while 75.0% (n = 129) of them presented a value below 12 and 12.2% (n = 21) above 18. In 15.2% of the included studies (n = 26), posterior R₀ showed a broad range of 95% CrIs, with the difference between lower and upper bounds exceeding 10. These R₀ estimates with a broad range tended to result from serosurveys with a smaller sample size, fewer age-specific data points, or conducted in the pre-vaccination era. Geographically, R₀ estimates concentrated in a range of less than 15 based on serosurveys conducted in the WHO Eastern Mediterranean Region, while in other regions, a few upper R₀ estimates could reach 30 and above. The variation in R₀ estimates remained large between studies in the same country, as seen in median R₀ estimates dispersing over a range of 20 in China, India, Brazil, and Türkiye (Fig J in S1 Appendix).

Across different study periods, age groups, and bias levels of serosurveys, pooled R₀ estimates mostly presented a right-skewed distribution and often peaked at a value <10 (Fig 2). However, R₀ estimates based on the same study feature could still have wide variation, as seen in the multimodal curves of pooled R₀ estimates in studies with a larger number of seroprevalence data points and a lower bias in sampling, measuring, and reporting measles serology. Our findings suggested that the survey period and age of populations may be associated with the peaks and shapes of pooled R₀ distributions. The median R₀ estimates were 8.99 (interquartile range (IQR)=10.4) in the serostudies conducted prior to 1990, 12.8 (IQR = 14.0) in 1991–2000, 4.48 (IQR = 3.62) in 2001–2010, and 5.17 (IQR = 3.73) in 2011–2019, showing a smaller value and narrower variability in the estimates based on more recent studies. A wider variation and a greater value were also found in R₀ estimates based on studies involving only children (median = 13.2, IQR = 11.6) compared to those with both children and adults (median = 5.19, IQR = 4.42). We also inspected six serostudies reporting R₀ below 1 and found they were conducted in near-elimination settings where MCV1 coverage level tended to be high and close to the overall seropositivity in the population. On the other hand, two serostudies with the highest R₀ values (>50) were conducted in the pre-vaccination era, where high seroprevalence in very young children was observed. The factors affecting the overall variation in R₀ remained important when we looked at influential factors for variation within countries. However, across different countries, the associated factors often had different directions of effect on R₀ (Fig K in S1 Appendix).

In exploring other country- and year-specific factors in the broader context, we identified a weak negative correlation (R = –0.2787, p = 0.0002) between the posterior median R₀ and Human Development Index, suggesting that measles transmissibility decreased with improvement in health and socioeconomics. We also found a weak positive correlation between median R₀ and average household size (R = 0.2437, p = 0.0015). Nonetheless, no significant correlation was found with population density (R = –0.0361, p = 0.6385). Based on the univariable log-linear regression analysis on R₀, HDI was a significant predictor but with limited explanation of the variance (R-squared = 3.93%, Fig 3).

WHO data on reported measles cases was not available, especially in the early years when case surveillance and notification systems had not yet been fully operated. Among 155 studies included for comparison (Fig L in S1 Appendix), 60% of our median model-based estimates (n = 93) show greater numbers than the WHO reported cases. Assuming these model-based estimates reflect the actual magnitude of measles incidence, we found that a proportion of 1.27% measles cases were reported to WHO (25^th–75^th percentiles: 0.56%–2.94%). However, in 36 studies for comparison, the upper bound model estimates reveal < 100 cases, while the WHO data reported > 1000 cases. We also noted that the majority of serostudies where model-estimated measles cases were lower than the WHO-reported cases were conducted in China (n = 23) and having severe bias in measuring and reporting serological results.

The comparison with the GBD 2021 Study was available for 134 serostudies (77.9%) conducted between 1988–2019 (Fig M in S1 Appendix). Our model-based case estimates generally differed from the GBD incidence estimates, with 84 serostudies (62.7%) having uncertainty intervals that did not overlap with those from GBD. Compared to GBD, our model was more likely to present lower case estimates and the scale of difference in median estimates was notable (lower by >80% for all 62 serostudies with non-overlapping interval estimates).

Fitting the DynaMICE model to the age-specific seroprevalence data, we presented a median RMSE of 6.16% (25^th–75^th percentiles: 2.40%–11.6%). Those serostudies with a poorer fit were with more age-specific data points for fitting, conducted in earlier years, and less likely to have low or moderate bias in overall serosurvey quality, but no particular trend was seen by WHO regions (Table B in S1 Appendix). We conducted a sensitivity analysis restricting the analysis to the 80% best-fitting studies, with RMSEs below 15.2%. Compared to the main analysis with a full set of studies, pooled R₀ estimates of the restricted set generally showed similar point estimates and wide intervals for WHO regions, study periods, age groups, and serological measurement and reporting biases (Fig 4).