Table 1 Dynamic model input parameters

Demographic parameters

Crude birth rate (B)

31.3–55.0 live births per 1000 per year, based on estimates for 1950–2035

[27]

Crude death rate (\(\mu\))

7.7–27.8 deaths per 1000 per year, based on estimates for 1950–2035^a

[27]

Disease parameters

Duration of infectiousness (\(1/\delta\)) (pre-outbreak)

3 weeks

[8, 28]

Assumes infections can be effectively treated with antibiotics

Seasonal offset parameter (timing of seasonal peak) (\(\phi\))

4.9 weeks (early February)

[8]

Based on timing of peak rainfall in Blantyre

Fraction infected who become chronic carriers (\(\theta\))

0.003–0.101 depending on age

[29]

We assume only first infections lead to chronic carriage

Disease-induced mortality (\(\alpha\))

0.001

[8, 30]

Duration of temporary full immunity to infection (\(1/\omega\))

104 weeks

[8, 28]

Pre-outbreak basic reproductive number (R₀)

3.29

Refit parameters from modified Pitzer et al. model [8]

Amplitude of seasonal forcing (q)

0.35

Refit parameters from modified Pitzer et al. model [8]

Relative infectiousness of chronic carriers (r)

0.09

Refit parameters from modified Pitzer et al. model [8]

Outbreak parameters^b

Beginning week of increase in duration of infectiousness (t₁)

April 10, 2011

Refit parameters from modified Pitzer et al. model [8]

End week of increase in duration of infectiousness (t₂)

November 23, 2014

Refit parameters from modified Pitzer et al. model [8]

Magnitude of increase in duration of infectiousness (m)

3.1954

Refit parameters from modified Pitzer et al. model [8]

Reporting process

Underreporting adjustment factor (a)

7.7 (95% CrI: 6.0–12.4)

[26]

Vaccine-related parameters

Age groups vaccinated

Based on WHO recommendation

 Routine

9 months

 Catch-up campaign

9 months to < 15 years

Initial efficacy of TCV against infection (\({\nu }_{0}\))

0.89 (95% CrI: 0.78–0.98)

Re-analysis based on Malawi TCV efficacy trial data and a previous estimate from [9, 23] (Additional file 1: S1.1.2.2. Text, Fig. S2)

Average duration of vaccine-induced immunity

(\(1/{\omega }_{v})\)

Vaccine efficacy decreases exponentially with an average duration of 18.9 (95% CrI: 8.4–83.3) years

Re-analysis based on Malawi TCV efficacy trial data and a previous estimate from [9, 23] (Additional file 1: S1.1.2.2. Text, Fig. S2)

Vaccine coverage

Gavi demand forecasts under assumption of unconstrained supply, and commonly assumed coverage during a catch-up campaign during an outbreak

 Routine (\({\kappa }_{R}\))

Increases from 0.85 to 0.95 over ten years

 Catch-up campaign (\({\kappa }_{C}\))

Uniform (0.6,0.9)