We constructed an agent-based dynamic transmission model of pneumococcal carriage and disease to explore some of the key determinants of the indirect effects of large-scale vaccination with pneumococcal conjugate vaccines (PCVs). Both of the principal types of indirect effects, herd immunity and serotype replacement, are mediated through the direct protective effect of vaccination on carriage, the source for pneumococcal transmission. Our findings are in agreement with earlier assertions that elimination of pneumococcal disease with serotypes included in the vaccine requires only a moderate direct efficacy against acquisition of carriage (e.g. Lipsitch, 1997). However, even in the event of elimination of vaccine-type (VT) invasive pneumococcal disease (IPD), there will be replacement disease whose incidence greatly depends on the disease causing propensity of the serotypes not included in the vaccine formulation.
This study corroborates to the notion that the transmission potential of pneumococcal carriage is moderate. Based on a susceptible–carrier–susceptible dynamics, we derived an approximate reproduction number R0
2 for an individual pneumococcal serotype. This value is broadly in line with a previous analysis of pneumococcal transmission in a population of mixing groups 
. Such a low reproduction number implies that carriage of the common serotypes can be effectively controlled by a reasonable direct impact of vaccination on carriage of the respective types, provided the coverage of vaccination is high ( and Figure S3.2 in File S3
). In a model-based study of the transmission dynamics of pneumococcal carriage and disease, an 86% coverage was enough for elimination of the vaccine types with vaccine efficacy against acquisition of the aggregate vaccine type at 76% and a waning rate of efficacy at 12% per year 
Assuming a negligible waning rate, the condition for obtaining herd immunity is pcc
, where c
is the vaccine efficacy against carriage and pc
is the coverage of vaccination 
. This inverse relation between pc
is clear also in the current setting () although the required efficacy and coverage are less than implied by the simple formula. This is obviously due to the fact that in a vaccinated population the non-vaccine types gain a fitness benefit which helps them to out-compete vaccine-type colonisation. This assertion is further supported by the finding that the model predictions about vaccine-type elimination did not depend on the assumed level of between-serotype competition (File S3
With a higher rate of waning (25%), the threshold moves towards higher values of pc
. The current knowledge about the duration of vaccine-induced protection against pneumococcal carriage is scarce. In a cross-sectional study among toddlers that had participated in a vaccine trial 3–4 years earlier, vaccine efficacy against VT carriage was approximately 40%, indicating a slow decline in vaccine-induced protection 
When elimination of vaccine types is reached, the pattern of serotype replacement in carriage is determined by the competitive interactions among the non-vaccine types (NVT), independently of vaccination-related parameters. Our model of between-serotype competition was constructed so that almost complete replacement of carriage occurs at the post-vaccination equilibrium, i.e., the incidence of NVT carriage in the new equilibrium is close to the overall incidence rate of all-type carriage in the pre-vaccination era. This feature corresponds to empirical observations from populations in which pneumococcal conjugate vaccine has been in large-scale use 
. Moreover, the relative proportions of the non-vaccine types as causes of carriage retained their pre-vaccination era relative magnitudes. Data from long-term surveillance of some vaccinated populations indicate that this may indeed be at least the first approximation of the distribution of serotypes in the post-vaccination era 
. Of note, given the ratio of the two competition parameters, the overall level and pattern of replacement in carriage were largely independent of their magnitudes ( and File S3
In addition to the new equilibrium in the incidence of carriage, replacement in disease (IPD) depends on the type- and age-specific case-to-carrier ratios. With increasing valency of the vaccine, the model projects a decreased IPD incidence among the target population of children <5 years of age and a longer time until near-elimination. Because of the different distribution of case-to-carrier ratios among the general population, the expected effect on the overall IPD incidence is milder. In particular, although category I with the three paediatric serotypes is clearly a major cause for IPD among children, it has a low case-to-carrier ratio among the general population compared to the case-to-carrier ratios of the categories of the replacing non-vaccine types.
To our knowledge, our model is the first agent-based dynamic model of pneumococcal carriage and disease which accommodates a large number of individual serotypes. Karlsson 
considered two aggregate types in an agent-based model to study the role of antibiotic use on pneumococcal transmission. Other approaches have been based on compartmental deterministic models. Effelterre et al. 
considered the effects of antibiotic use and vaccination in children less than 2 years of age, based on a dynamic model for 18 serotypes or groups. Melegaro et al. 
investigated the long-term effectiveness of PCV7 vaccination in the UK. Their model was based on pooling the vaccine types and non-vaccine serotypes into two aggregate types and calibrating the efficacy and duration vaccine-induced protection against carriage to produce the post-vaccination pattern of herd immunity and serotype replacement in the US, i.e., in another population after the introduction of PCV7. The calibration of an updated model was based on 3-year post-vaccination surveillance of IPD in the UK 
. Of note, the model in the present paper was calibrated using pre-vaccination data in a single population. The efficacy and duration of vaccine-induced protection against carriage were free control parameters in post-vaccination projections of carriage and disease ().
Clearly, building a dynamic transmission model which would address the more than 90 pneumococcal serotypes individually is both impractical and unnecessary. Some kind of pooling of serotypes is called for. Our approach is based on splitting of both the vaccine and non-vaccine groups of serotypes, corresponding to each PCV formulation, into individual types or subcategories. This feature has important implications. First, pooling serotypes simply into vaccine and non-vaccine types would create two “super-types”, with an overestimated overall rate of acquisition for the vaccine types. This might translate into exaggerated claims of the required vaccination effort for elimination of vaccine-type carriage and disease. Second, the nearly complete replacement of carriage cannot be easily reproduced with a model with only two types. By contrast, our model with 11 competing model types reproduces this phenomenon. Third, any projections on the post-vaccination pattern of IPD based on two types could be biased due to the lack of any detail regarding the rate and pattern of carriage. Furthermore, the additional cost of including more than two types into the model is minimal, with only two parameters required to parameterise the between serotype competition. Our simple empirical model of competition among the serotypes is consistent with the hypothesis that the polysaccharide capsule (i.e., serotype) may affect the fitness of the bacterium in competition with other serotypes during colonisation 
The mixing pattern induced by the demographic characteristics implemented in our model emphasizes the importance of contacts among children in families, day care centres and schools and contacts between parents and their children. This is in agreement with strong assortative contact patterns found elsewhere 
Potential caveats in our model assumptions include the stability of the serotype distribution by age and the homogeneity of vaccine protection against all vaccine types. The distribution of serotypes was based on data about pneumococcal carriage in children less than 2 years of age (; 
). It is possible that the dominant serotypes are different in older children or adults 
although the scarcity of data declined a conclusive analysis of this in the current setting. The threshold for VT elimination is likely to be robust to slight misspecifications of the serotype distribution in adults because of the importance of the younger age classes in sustaining transmission. By contrast, the projected IPD incidence in adults could be more prone to bias due to biased rates of acquisition and case-to-carrier ratios. For example, if the actual proportion of non-vaccine serotypes in adults is larger than in the model, the corresponding case-to-carrier ratios in our analysis would be over-estimates. This would lead to exaggerated predictions on replacement disease in adults so that the 22% increase in IPD under use of PCV7 () would be pessimistic. This problem is likely to be largest with PCV7, which covers serotypes commonly carried by children. An analogous argument applies to biases induced by the assumed similarity of serotype-specific clearance rates. For example, if some non-vaccine serotypes are carried for clearly shorter times than in the model, the estimated acquisition rates would be under-estimates and, subsequently, the case-to-carrier ratios over-estimates. This could lead to over-estimates of replacement disease by such serotypes.
The vaccine efficacy against acquisition of carriage was assumed to have the same value for all vaccine serotypes. Although there maybe differences in efficacy between individual serotypes, the overall efficacy against serotypes in various PCV formulations appears to be somewhere about 50% 
. The current findings can therefore be expected to hold for most vaccine serotypes. Vaccine-induced cross-protection was not considered in the model although some serotypes may be affected by cross-reactive immunity, serotype 6A being the most frequently carried and an important source of replacement. However, the data in this study did not differentiate between serotypes 6A (potential cross-immunity) and 6C (no cross-immunity) which were formerly both classified as 6A 
. The inclusion of 6A as an NVT in the analyses for PCV7 and PCV10 is likely to lead to too low IPD predictions, based on the relative importance of 6A as cause of carriage and its low case-to-carrier ratio. The possibility for capsular switching was also not featured in our model. However, its impact on pneumococcal population has been suggested to be minor in comparison to serotype expansion caused by reduced competition by the vaccine types 
The vaccine-induced protection was not assumed to take effect until the booster dose at 12 months of age. This model feature excludes the possibility to address questions about the impact of different schedules and dosage of vaccination. However, model-based predictions about the indirect effects and the net effectiveness of vaccination depend on the assumed vaccine efficacy against acquisition and the waning rate of protection. Assuming protection only after 12 months represents a conservative approximation, should there be considerable protection starting during the earlier phase of the schedule.
One of the key questions about the long-term effectiveness of pneumococcal vaccination concerns the extent and pattern of serotype replacement in different disease manifestations. In this study, of the possible manifestations of pneumococcal disease, we only considered invasive pneumococcal disease. This was because of the relatively sensitive and specific data on the incidence of IPD in Finland. Acute otitis media (AOM) and mild respiratory infections are probably not of interest because of rapid replacement of carriage in the long-term. The question of pneumococcal pneumonia remains to be tackled, in particular in developing country settings where it is thought to constitute the main burden of pneumococcal disease. The current micro-simulation approach offers a suitable platform for such extensions.