The human pathogen Streptococcus pneumoniae is a major cause of diseases, including pneumonia and meningitis. The introduction of multi-valent vaccines against S. pneumoniae successfully reduced the burden of disease and the prevalence of targeted strains. However, untargeted S. pneumoniae strains have benefitted from the vaccine introduction as over time they replace the targeted strains. To prevent the rise of pathogenic strains, it is crucial to understand which of the untargeted S. pneumoniae strains will dominate the replacement. This strain replacement can be modelled through negative frequency-dependent selection (NFDS) on the genome content. NFDS is a type of balancing selection for which the benefit of a given trait negatively correlates with the prevalence of that trait within a population. By extending a previously published model, we developed a faster and more flexible mathematical model that describes the post-vaccine dynamics of S. pneumoniae populations. Our model reliably identifies S. pneumoniae strains which increase in prevalence. The model is faster and easier to reuse than previous implementations, and the use of modern bioinformatic tools facilitates the application and reuse in other datasets and species. The model output can be used to predict burden of disease, advise policy decisions, and inform future vaccine design.