Fitting the DynaMICE model to the 172 seroprevalence studies using Markov Chain Monte Carlo (MCMC), we obtained 500 sets of posterior parameters from the converged chains. The posterior model estimates of age-specific seroprevalence show a good fit using the root mean square error (RMSE) measure, with two-thirds of the studies having an average difference less than 10% between the model results and observed data. There was a positive correlation between median R ₀ and vaccine effectiveness estimates (Spearman’s correlation coefficient (R)=0.444, p-value (p) <0.001. However, the correlation became weaker after excluding studies with a severe or critical bias in study population selection, serological measurement and result reporting (R=0.380, p=0.003). No significant correlation between R ₀ and duration of maternal immunity was found (R=0.032, p=0.680).

Figure 1 presents the median and 95% credible intervals (CrIs) of the R ₀ posterior distributions obtained from fitting the DynaMICE model to age-specific seroprevalence data in 172 individual studies. We observed a right skewed distribution of R ₀ estimates, ranging widely across studies from 0.94 (95% CrI: 0.73–1.00) to 154 (95%CrI: 69.8–212). Only 18% (n=31) of the median estimates were in the commonly cited range of 12–18, ³ while 70% (n=121) of them presented a value below 12 and 12% (n=20) above 18. In 21% of the included studies (n=35), posterior R ₀ showed a broad range of 95% CrIs, with the difference between lower and upper bounds exceeding 10. These R ₀ estimates with a broad range tended to result from serosurveys with a smaller sample size, fewer categories of age groups, or conducted in the pre-vaccination era. Geographically, R ₀ estimates concentrated at a range of less than 15 based on serosurveys conducted in the World Health Organization (WHO) Eastern Mediterranean Region, while in other regions, estimates of ≥30. The variation of R ₀ estimates remained large between studies in the same country, as seen in China, India, Brazil, and Türkiye, where median R ₀ estimates disperse over a range of 20 in each country.

Across different study periods, age groups, and bias levels of serosurveys, pooled R ₀ estimates mostly presented a right-skewed distribution and often peaked at a value <10 ( Figure 2). However, R ₀ estimates based on the same study feature could still have wide variation, as seen in the multimodal curves of pooled R ₀ estimates in studies with a larger number of seroprevalence data points and low 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 R ₀ distributions. The median R ₀ estimates were 8.23 (interquartile range (IQR)=10.2) in the serostudies conducted prior to 1990, 13.0 (IQR=13.0) in 1991–2000, 5.50 (IQR=5.76) in 2001–2010, and 6.39 (IQR=5.42) 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 R ₀ estimates based on the studies involving only children (median=13.0, IQR=12.1) compared to those with both children and adults (median=6.43, IQR=7.24).

In exploring other country- and year-specific factors in the broader context, we identified a weak negative correlation (R=–0.1917, p=0.0117) between the posterior median R ₀ and Human Development Index, suggesting that measles transmissibility decreased with improvement in health and socioeconomics. Nonetheless, no significant correlation was found between median R ₀ and average household size (R=0.1472, p=0.0577) or population density (R=–0.0181, p=0.8139). Based on the univariate log-linear regression analysis on R ₀, Human Development Index (HDI) was a significant predictor but with limited explanation of the variance (R-squared=2.3%, Figure 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, 60% of our median model-based estimates (n=93) show greater numbers than the reported cases. Assuming these model-based estimates to reflect the actual magnitude of measles incidence, we found a proportion of 1.27% measles cases were reported to WHO (25 ^th–75 ^th percentiles: 0.56%–2.94%). However, in 32 studies, we estimated fewer than 100 cases with upper bound model estimates, while the WHO data reported more than 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=18) and having severe bias in measuring and reporting serological results.

The comparison with the Global Burden of Disease (GBD) 2021 Study was available for 134 studies (78%) conducted between 1988–2019. Our model-based case estimates did not show consistent prediction trends with the GBD incidence estimates, with 60% of included studies having no overlapping between the two interval estimates.

Fitting the DynaMICE model to the age-specific seroprevalence data, we presented a median RMSE of 6.93% (25 ^th–75 ^th percentiles: 3.37%–12.2%). The sensitivity analysis was restricted to the top 80% best-fit studies, where RMSEs are less than 14.5%. Compared to the main analysis with a full set of studies, pooled R ₀ estimates of the restricted studies showed consistent magnitude and wide intervals for WHO regions, study period, age groups, and serological measurement and reporting biases ( Figure 4).

We obtained 221 articles from a 2024 systematic review by Sbarra et al. that summarised the scope and bias in population-level measles serosurveys. ¹⁸ 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, ¹⁸ we excluded surveys having a critical bias in the representativeness of the study populations and 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. 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 very 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. 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%).

We fitted DynaMICE to each unique set of age-specific seroprevalence data per country-time period using MCMC with component-wise Metropolis algorithm and random order for updating parameters in each blocked iteration. ²¹ Three parameters—R ₀, duration of maternal immunity protection, and vaccine effectiveness for the first dose of measles-containing vaccine (MCV)—were varied. These parameters were assumed to be constant over time within the same seroprevalence study and were drawn from prior distributions based on previous literature ( Table 1). For 69 serosurveys conducted prior to country-specific MCV introduction, we removed the parameter for vaccine effectiveness and fit 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 ran two chains with different starting parameter values and conducted diagnostic checks for convergence of chains and goodness of fit. We obtained 500 posterior samples for each study and calculated their medians and 95% CrI. All analysis and visualisation were conducted in R 4.2.3, and the computer codes can be found at https://zenodo.org/records/15424461.

In our model-based outputs, we added up the non-susceptible populations—maternally immune, infectious, and recovered sub-populations (compartments) ⁷ 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. For a given parameter set, models were first simulated using the country-specific demographics in 1980 ²² and assumed no implementation of vaccination until they reached equilibrium, and then begun with annual inputs of demographics and national-level MCV coverage estimates ¹ from 1980, when the coverage data is earliest available. For serosurveys conducted before 1980, we extracted the model estimates in 1980, assuming that seroprevalence was likely similar during earlier years given low coverage of vaccination and other control measures for measles.

Measles R ₀ 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 of measles R ₀. In addition, the survey quality and available details of seroprevalence data also affect the estimation of R ₀ through fitting to seroprevalence data. To understand these dependencies, we evaluated the association between R ₀ estimates and different study features, including survey period, age of the survey population, number of age-specific data points, and biases in sampling, measurement and reporting serology. ¹⁸ By drawing 10,000 bootstrapped samples with replacement, we pooled R ₀ estimates in studies with the same selected categories and compared their distributions.

We assessed the association of median R ₀ for each study with average household size, ²³ population density, ²² and HDI. ²⁴ 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 imputed the HDI value at the closest year on a country basis.

Using the posterior parameters of R ₀, 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 ²⁵ to assess their consistency in measuring measles burden and the potential issue of underreporting. We also compared our model-based estimates to measles incidence estimates in the GBD Study 2021, ²⁶ as it is the 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 RMSE between the observed seroprevalence data and median posterior predictions at specified age groups in each study. To assess how model fit affects the estimation of R ₀, we ranked the RMSE and conducted a sensitivity analysis on the pooled R ₀ results after removing 20% of the studies with the highest error size.