Fig. 1.

Model structure flow diagram. The epidemiological states include individuals that are susceptible (non-carrying), $S$; carry a vaccine serotype, $V$; carry a weak non-vaccine serotype, $N_w$; carry a strong non-vaccine serotype, $N_s$; carry simultaneously a weak and a strong non-vaccine serotype, $N_{\mathit{sw}}$; carry simultaneously a vaccine serotype and a weak non-vaccine serotype, $B_w$; or carry simultaneously a vaccine serotype and a strong non-vaccine serotype, $B_s$ (see text). Once vaccinated, the individual moves to one of the corresponding states, $(S^{(v)}\text{,}{V}^{(v)}\text{,}{N}_w^{(v)}\text{,}{N}_s^{(v)}\text{,}{B}_w^{(v)}{\mathit{andB}}_s^{(v)})$. The acquisition rates from the single to multiple serotype carriage states are reduced by competition parameters denoted by $c$ with two subscripts; the first denoting the serotype group ($v\text{,}s\mathit{and}w$, for VT, strong NVT and weak NVT respectively) of the resident serotypes and the second denoting the age-group. The competition parameters have two sets of values, one for age group <6 and another for age group ≥6 years (see text). The age-group specific VT, weak NVT and strong NVT clearance rates are denoted by ${\text{r}}_{\text{Vi}}\text{,}{\text{r}}_{\text{Nwi}}$ and ${\text{r}}_{\text{Nsi}}$, respectively. In addition to the transitions between the 14 epidemiological states as shown in the figure, individuals die from any states at age-specific death rates and new individuals are born into the completely susceptible state.