Additional file 1 of The impact of local vaccine coverage and recent incidence on measles transmission in France between 2009 and 2018
Creators: name: Robert, Alexis
name: Kucharski, Adam J.
name: Funk, Sebastian
Publisher: name: figshare
Year: 2022
Subjects: subject: Medicine
subject: Biotechnology
subject: 59999 Environmental Sciences not elsewhere classified
subject: FOS: Earth and related environmental sciences
subject: Ecology
subject: FOS: Biological sciences
subject: Immunology
subject: FOS: Clinical medicine
subject: 69999 Biological Sciences not elsewhere classified
subject: 19999 Mathematical Sciences not elsewhere classified
subject: FOS: Mathematics
subject: Cancer
subject: 110309 Infectious Diseases
subject: FOS: Health sciences
subject: Computational Biology

description: Additional file 1: Figure S1. Estimates of the parameters in each component of Model 1, using the reference fit (grey) and ten different values of the composite interval (orange). unvax corresponds to the effect of ui, t, the mean proportion unvaccinated over the three years before t in i; incid1 and incid2 correspond to the effect of $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^1$$ N i , t 1 and $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^2$$ N i , t 2 the category of incidence in the three years before t in i; pop corresponds to the effect of mi, t the number of inhabitants at t in i; area corresponds to the effect of the surface; sin and cos correspond to the effects of seasonality; distance and population correspond to the spatial parameters of the connectivity matrix ω (δ and γ); overdisp is the estimate of the log-overdispersion parameter in the negative binomial distribution of Yi, t. Dots show the mean values associated with the parameters; arrows show the 95% Confidence interval. The orange arrows indicate the extreme values of the 95% confidence interval obtained using different distributions of the composite serial intervals. Figure S2. Estimates of the parameters in each component of Model 2, using the reference fit (grey) and ten different values of the composite interval (orange). unvax corresponds to the effect of ui, t, the mean proportion unvaccinated over the three years before t in i; incid1 and incid2 correspond to the effect of $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^1$$ N i , t 1 and $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^2$$ N i , t 2 the category of incidence in the three years before t in i; pop corresponds to the effect of mi, t the number of inhabitants at t in i; area corresponds to the effect of the surface; sin and cos correspond to the effects of seasonality; distance and population correspond to the spatial parameters of the connectivity matrix ω (δ and γ); overdisp is the estimate of the log-overdispersion parameter in the negative binomial distribution of Yi, t. Dots show the mean values associated with the parameters; arrows show the 95% Confidence interval. The orange arrows indicate the extreme values of the 95% confidence interval obtained using different distributions of the composite serial intervals. Figure S3. Temporal and spatial distribution of the missing data: Panel A: Number of missing observations per year, missing coverage in 2004 and 2005 did not need to be inferred in the model, and since 2009 was entirely missing, we did not infer any value that year. Panel B: Number of missing entries per region. Figure S4. Panel A: Values of the three parameters of the regression for each region. Panel B: Estimated values of coverage between 2004 and 2017, the dots represent the mean estimate, shaded areas correspond to the 95% Confidence Intervals. The purple, orange and green areas representing three departments illustrate how the changes through time can differ depending on the region. Figure S5. Diagnosis of the regression on the vaccine coverage. Left panel: Fitted vs residuals plot, Left panel: uniform quantile-quantile plot. Figure S6. Distribution of the residuals per year of inference. The blue line indicates the mean value every year. Figure S7. Estimates of the parameters in each component of Model 1, using the reference fit (grey) and 100 different values of coverage for the inferred entries (orange). unvax corresponds to the effect of ui, t, the mean proportion unvaccinated over the three years before t in i; incid 1 and incid2 correspond to the effect of $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^1$$ N i , t 1 and $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^2$$ N i , t 2 the category of incidence in the three years before t in i; pop corresponds to the effect of mi, t the number of inhabitants at t in i; area corresponds to the effect of the surface; sin and cos correspond to the effects of seasonality; distance and population correspond to the spatial parameters of the connectivity matrix ω (δ and γ); overdisp is the estimate of the log-overdispersion parameter in the negative binomial distribution of Yi, t. Dots show the mean values associated with the parameters; arrows show the 95% Confidence interval. The orange arrows indicate the extreme values of the 95% confidence interval obtained drawing different values of coverage for the missing entries. Figure S8. Estimates of the parameters in each component of Model 2, using the reference fit (grey) and 100 different values of coverage for the inferred entries (orange). unvax corresponds to the effect of ui, t, the mean proportion unvaccinated over the three years before t in i; incid1 and incid2 correspond to the effect of $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^1$$ N i , t 1 and $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^2$$ N i , t 2 the category of incidence in the three years before t in i; pop corresponds to the effect of mi, t the number of inhabitants at t in i; area corresponds to the effect of the surface; sin and cos correspond to the effects of seasonality; distance and population correspond to the spatial parameters of the connectivity matrix ω (δ and γ in Equation X); overdisp is the estimate of the log-overdispersion parameter in the negative binomial distribution of Yi, t. Dots show the mean values associated with the parameters; arrows show the 95% Confidence interval. The orange arrows indicate the extreme values of the 95% confidence interval obtained drawing different values of coverage for the missing entries. Figure S9. Estimates of the parameters in each component of Model 1 (blue) and Model 2 (purple): Panel A: Autoregressive component; Panel B: Neighbourhood component; Panel C: Endemic component; Panel D: Other coefficients. The y-axis. unvax corresponds to the effect of ui, t, the mean proportion unvaccinated over the three years before t in i; incid1 and incid2 correspond to the effect of $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^1$$ N i , t 1 and $${\mathrm{N}}_{\mathrm{i},\mathrm{t}}^2$$ N i , t 2 the category of incidence in the three years before t in i compared to the level of reference (i.e. $${\mathrm{N}}_{0,\mathrm{t}}^0$$ N 0 , t 0 ); pop corresponds to the effect of mi, t the number of inhabitants at t in i; area corresponds to the effect of the surface; sin and cos correspond to the effects of seasonality; distance and population correspond to the spatial parameters of the connectivity matrix ω (δ and γ); overdisp is the estimate of the log-overdispersion parameter in the negative binomial distribution of Yi, t. Dots show the mean values associated with the parameters; arrows show the 95% Confidence interval. Note different y-axes between graphs. Figure S10. Estimates of the parameters in each component of Model 1 (blue) and Model 2 (purple): Panel A: Autoregressive component; Panel B: Neighbourhood component; Panel C: Endemic component; Panel D: Other coefficients. The y-axis. unvax corresponds to the effect of ui, t, the mean proportion unvaccinated over the three years before t in i; incid correspond to the effect of increasing the incidence in the three years before t in i; pop corresponds to the effect of mi, t the number of inhabitants at t in i; area corresponds to the effect of the surface; sin and cos correspond to the effects of seasonality; distance and population correspond to the spatial parameters of the connectivity matrix ω (δ and γ); overdisp is the estimate of the log-overdispersion parameter in the negative binomial distribution of Yi, t. Dots show the mean values associated with the parameters; arrows show the 95% Confidence interval. Note different y-axes between graphs. Figure S11. Seasonality of each component in Model 1 (Panel A) and Model 2 (Panel B). We quantified the impact of seasonality using the percent of variation around the mean value every day. Figure S12. Panel A and B: Daily and weekly fit between the data and Model 2. The inferred number of cases is split among the three components of the model. Panel C to F: PIT histograms of Model 2, generated respectively for predictions 3, 7, 10, and 14 days ahead. Figure S13. Comparison between predictions 3, 7, 10, and 14 days ahead using model 1 and model 2 and the data. Lines correspond to the median estimates, shaded areas correspond to the 95% predictions intervals. The blue and purple predictions are similar for the entire calibration period, hence the curves overlap in all panels. Black dots represent the number of cases 3, 7, 10, and 14 days ahead in France at each date. Figure S14. Proportion of cases per component in both models. Figure S15. Percentage of simulations where the number of cases reported in each region in 2019 was at least 1, 10, and 50 cases for each scenario using parameter estimates from Model 2. Each row corresponds to a different scenario: i) Reference, ii) Minimum level of recent incidence in each region, iii) Local vaccine coverage increased by 3% in each region, iv) Local vaccine coverage decreased by 3% in each region. Figure S16. Percentage of simulations where the number of cases reported in each region in 2019 was at least 1, 10, and 50 cases following the importations of ten cases in December 2018, and using the parameter estimates from Model 2. For each row, the region of importation is indicated by a black dot. Figure S17. Geographic distribution of the number of inhabitants (right panel), average vaccine coverage (central panel), and recent incidence (left panel) at the end of 2018. Figure S18. Percentage of simulations where the number of cases reported in each region in 2019 was at least 1, 10, and 50 cases following the importations of ten cases in December 2018, and using the parameter estimates from Model 1 and a three percent decrease in vaccine coverage in each region. For each row, the region of importation is indicated by a black dot. Figure S19. Percentage of simulations where the number of cases reported in each region in 2019 was at least 1, 10, and 50 cases following the importations of ten cases in December 2018, and using the parameter estimates from Model 1 and a three percent increase in vaccine coverage in each region. For each row, the region of importation is indicated by a black dot. Figure S20. Sharpness, bias and RPS scores of the Daily model with and without Random Effects (RE), and of the aggregated model. Figure S21. Number of cases by day of the week. We used the onset date for each case reported to the ECDC between 2009 and 2018. Figure S22. Comparison of the parameter estimates obtained in Model 1 (similar to Fig. 2) with or without a weekday covariate added in each compartment. Weekday was computed as a binary covariate, whose value was 1 on Saturdays and Sundays, and 0 otherwise.