Figure 1. Susceptible-Infected-Susceptible (SIS) model structure.

SIS model structure for estimating the forces of infection for vaccine types and non-vaccine types. Abbreviations: λ_N, age-dependent forces of infection for non-vaccine types; λ_V, age-dependent forces of infection for vaccine types; B, both vaccine types and non-vaccine types co-colonised; c_N, competition parameters that determined the relative risk of acquiring non-vaccine types if already colonised by vaccine types; c_V, competition parameters that determined the relative risk of acquiring vaccine types if already colonised by non-vaccine types; i, age group; N, non-vaccine types carriers; r_N, recovery rate for non-vaccine types; r_V, recovery rate for vaccine types; S, susceptible; V, vaccine type carriers;.