The swine gut microbiota is a complex ecosystem found throughout the gastrointestinal tract, with multiple exchanges with the host and whose composition is linked to both external and internal factors, such as diet or breed. Diet, probiotic, or prebiotic interventions have been designed to boost beneficial host-microbiota interactions, such as the production of anti-inflammatory molecules, or the fermentation of otherwise undigested resources. In parallel, a smaller microbial population, shared among the same host species, independent of external or internal factors, has been described and defined as the "core microbiota." Therapies targeting the core microbiota could possibly lead to more precise and long-lasting effects. However, the metabolic role of the porcine core microbiota, especially in relation to the rest of the microbial community, is currently missing. We present here the first dynamic model of the porcine core microbiota, which we used to estimate the core-microbiota metabolite production and to forecast the effect of a synbiotic intervention targeting the core genera of the core microbiota. We developed a community model in which a total of 17 microbial groups were established based on culture-based information of representative species. First, the model parameters were estimated, and the resulting model simulations were compared favorably with in vitro experimentation. The model was then used to predict the microbial dynamics of the core and non-core members under different experimental conditions. Therefore, it was able to theorize the main-metabolite core microbiota contribution, hypothesizing that it could be mainly responsible for acetate and propionate, but not for butyrate production.