MATHEMATICAL MODELS TO EVALUATE THE PROBIOTIC EFFECT ON THE RUMINANT DIGESTIVE SYSTEM

To investigate probiotic, rumen, and host digestive physiology interactions, mathematical models are effective. These models measure how probiotics alter ruminant pH, microbial proliferation, and nutrient absorption. Mathematical models for ruminant digestive system probiotic effects are reviewed in this work. The effects of probiotics on ruminants' digestive tracts are studied using mathematical models that account for biological processes, microbial interactions, and nutritional metabolism. These models can separate rumen, intestinal, and probiotic colonization processes. These models predict probiotic strain growth, food metabolism, host-microbe interactions, parameterization, and validation. Rumen bacteria, protozoa, fungus, and archaea break down complex plant components for digestion. Explaining and predicting probiotic effects requires mathematical models of microbial growth and fermentation. Microbial growth and fermentation optimize digestive efficiency and health, and dynamic models address time-dependent microbial population and substrate concentration variations. Estimating probiotic strain counts and rumen microbe interactions requires models. VFA and methane production are used to evaluate probiotic therapy. To maximize effects, probiotic therapy time and dose are optimized. The Monod Kinetics model investigates cellulolytic bacteria that degrade rumen fiber. This model depicts how probiotics break down hemicellulose and cellulose to help ruminants utilize vegetable nutrients. Colonic Lactobacillus species, especially lactate-producing ones, are studied under the Gompertz model. Dynamic modeling of rumen microbial interactions helps explain and predict probiotic effects on fermentation. The model shows how feeding A. bovis probiotics impacts rumen microbial populations and fermentation products. The simulation reveals increased cellulolytic bacterial populations, substrate use, VFA production, and pH stability. Enhanced fiber degradation, cellulose utilization, total VFA generation, and pH stability. Finally, simulations show how probiotics alter rumen fermentation, boosting nutrition and greenhouse gas mitigation. Complete probiotic effects on the ruminant digestive system can be assessed using multi-scale models. This method models complex rumen interactions at the molecular, cellular, and ecological levels. Multiscale research from microbial kinetics to animal performance can help researchers understand how probiotics effect rumen fermentation, nutrient absorption, and animal health. Molecular, cellular, ecological, and animal scales are modelled. The integration plan includes model coupling, data flow, feedback loops, and animal performance data to improve ecological and cellular models. Experimental data calibrates model parameters at all scales, whereas simulations show dynamic changes over time.