Table 1.
Overview of the seven serotype groups defined in the model.
Fig 1.
Scheme of the epidemiological model.
We assumed acquisition and loss of carriage to be stepwise processes, i.e., non-carriers can become single carriers, who can become double carriers or non-carriers again; double carriers first become single carriers before becoming non-carriers again. For a detailed description see text. S: non-carriers; G1,…,G7: carriers of serotype group 1,…,7; G1G2,…,G6G7: double carriers (2 serotype groups); i = 1,…,400: age stratum; λG1,…,λG7: age-dependent transmission risks; c12,…,c76: competition parameters; r: age-dependent rates of loss of carriage.
Fig 2.
Scheme of the vaccination model.
The model is an extension of the epidemiological model depicted in Fig 1. Three different states were distinguished: individuals can be unvaccinated or vaccinated with either PCV7 or PCV13. Transitions between states were described via vaccination and waning rates. For a detailed description see text. S: non-carriers; G1,…,G7: carriers of serotype group 1,…,7; G1G2,…,G6G7: double carriers (2 serotype groups); I = 1,…,400: age stratum.
Fig 3.
Results of the fitting process of the basic epidemiological model (i.e., without vaccinations).
Initializing the model with arbitrary starting values, the model system was simulated for 50 years until a steady-state in all compartments was reached. The rightmost timepoint corresponds to the epidemiological year 2005/06 (pre-PCV vaccinations), where the agreement between model and data points (pneumococcal carriage proportions in Germany) was optimized. While the results are depicted separately for each serotype group (figure headings), age groups are visualized by colors: black (<2y), red (2-4y), green (5-15y), blue (16-44y), cyan (45-59y), purple (60-74y), yellow (75-84y), gray (≥85y). Model oscillations due to the assumption of simultaneous aging were smoothed out.
Table 2.
Estimated parameters of the vaccination model (with 95% CIs) in percent.
Fig 4.
Predictions of vaccination model for children aged <2y.
Shown are vaccine serotype groups (upper row) PCV7 (A), PCV13 non-PCV7–3 +6C (B), serotype 3 (C), and non-vaccine serotype groups (lower row) PCV15 non-PCV13 (D), PCV20 non-PCV15 (E), PPSV23 non-PCV20 (F), and Other (G). Data points (pneumococcal carriage proportions regarding all individuals of the age group in Germany, including non-carriers) are shown as filled circles with 95% CIs. Data points were calculated from adjusted IPD incidence rates via case-carrier ratios. Simulation results are depicted by lines with shaded 95% prediction intervals. The wide shades observed for PCV7 and PCV13 non-PCV7–3 +6C are caused by uncertainty of direct vaccination effects while the variability observed in non-vaccine serotype groups is indirect. Thus, respective prediction intervals are narrower.
Fig 5.
Predictions of vaccination model for adults aged 60-74y.
Shown are vaccine serotype groups (upper row) PCV7 (A), PCV13 non-PCV7–3 +6C (B), serotype 3 (C), and non-vaccine serotype groups (lower row) PCV15 non-PCV13 (D), PCV20 non-PCV15 (E), PPSV23 non-PCV20 (F), and Other (G). Data points (pneumococcal carriage proportions regarding to all individuals of the age group in Germany, including non-carriers) are shown as filled circles with 95% CIs. Data points were calculated from adjusted IPD incidence rates via case-carrier ratios. Lines with shaded 95% prediction intervals depict simulation results.
Fig 6.
Stacked bar plots of predicted absolute IPD cases per year from 2006 to 2031 in Germany for three different age groups (<2y, 16-59y, ≥60y).
The stacked bars illustrate the serotype groups defined in Table 1: PCV7 (G1; light blue), PCV13 non-PCV7–3 +6C (G2; red), serotype 3 only (G3; dark green), PCV15 non-PCV13 (G4; purple), PCV20 non-PCV15 (G5; cyan), PPSV23 non-PCV20 (G6; gray), Other serotypes (G7; light green). Heights of the individual bars correspond to the average model prediction without considering sensitivity of the model parameters (i.e., prediction intervals). Data points (reported IPD case numbers in Germany multiplied by an estimated year-specific underreporting factor) are shown as filled circles with 95% CIs. Age group 16-59y combines two (16-44y, 45-59y) and age group ≥60y combines three (60-74y, 75-84y, ≥85y) age groups of the model.
Fig 7.
Prediction of absolute IPD cases per year from 2006 to 2031 in Germany for three different vaccine serotype groups (PCV13, PCV15, PCV20; rows) and three age groups (<2y, 16-59y, ≥60y; columns).
In this figure, vaccine serotype groups are defined additively: PCV13 (green) is defined as the sum of G1 (PCV7), G2 (PCV13 non-PCV7–3 +6C), and G3 (serotype 3 only). PCV15: G1+G2+G3+G4 (orange), PCV20: G1+G2+G3+G4+G5 (blue). Serotype 6C is additionally included in each group, because it was included in the G2 group (Table 1). As in Fig 6, age group 16-59y combines two (16-44y, 45-59y) and age group ≥60y combines three (60-74y, 75-84y, ≥85y) age groups of the model. Data points (reported IPD cases in Germany multiplied by year-specific underreporting factor) are depicted as filled circles with 95% CIs. Average model predictions are shown by lines with shaded 95% prediction intervals accounting for sensitivity of the model parameters.