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Abstract Infection with pnuemococcus bacteria is generally mild but can be more severe in the young and elderly, causing invasive pneumococcal disease (IPD) and community-acquired pneumonia (CAP). Although paediatric pneumococcal conjugate vaccine (PCV) programmes and elderly pneumococcal polysaccharide vaccine (PPV) programmes have reduced cases, we estimate that pneumococcal infection still leads to direct health care costs of around £68M and approximately 16 thousand QALY losses in England per year. The public health situation is complicated by the large number of interacting serotypes, such that while serotype-specific vaccines reduced the target serotypes others arose to replace them. Here we develop a novel (relatively) low-dimensional model to capture the interaction of 26 common pneumococcal serotypes. The model is matched to English IPD data from 2000-2023 and to five carriage studies (conducted in 2001/02, 2008, 2012, 2015 and 2018). When combined with a health economic approach, this model allows us to calculate the willingness to pay for paediatric vaccination with PCV7 (introduced in England in 2006), PCV13 (introduced in England in 2010) and the future vaccination of both the young and elderly with PCV20, which offers protection against 20 serotypes. Due to rapid serotype replacement, we find that the introduction of PCV7 vaccination in 2006 was not cost effective - a result that could not have been anticipated at the time, but is supported by simple statistical fits to the IPD data. In contrast, switching to PCV13 in 2010 and switching to PCV20 in 2026 are both associated with a high willingness to pay for a single dose. Given pneumococcal disease has shifted over time to become predominantly in the older adult population, we find that switching from PPV23 to PCV20 vaccination in those aged 65 and introducing an additional PCV20 vaccine at age 75 are both cost effective for a sufficiently low vaccine price. The inference that underpins our model is unfortunately limited by the available data and the high-dimensional nature of multiple interacting serotypes. Future sampling of carriage from older adults would greatly improve our confidence, as would national estimates of CAP.