Bistability and Hysteresis in Gut Dysbiosis: A Spatiotemporal Mathematical Framework Integrating Phage Dynamics and Metabolic Feedback

The transition from intestinal eubiosis to dysbiosis represents a critical phase shift in a complex adaptive ecosystem, often characterized by hysteresis and resistance to reversal. This manuscript advances beyond descriptive frameworks to propose a rigorous, falsifiable mathematical model of gut microbiota dynamics. We integrate Generalized Lotka-Volterra (gLV) equations with reaction-diffusion terms to account for spatial heterogeneity along the luminal-mucosal axis. Furthermore, we introduce a coupled metabolic feedback loop linking Short-Chain Fatty Acid (SCFA) concentrations to microbial resilience and explicitly model bacteriophage-host predator-prey dynamics as a mechanism for targeted therapeutic intervention. The model is calibrated using parameters derived from human metagenomic datasets (e.g., GMrepo and Human Microbiome Project), including time-series abundance data for beneficial (e.g., Faecalibacterium prausnitzii) and harmful (e.g., Escherichia coli) bacteria in IBD patients versus healthy controls. We delineate a multi-stage therapeutic protocol that leverages the concept of "tipping points," proposing that successful treatment requires pushing the ecosystem across a separatrix of bistability. This framework provides reproducible Python code for simulation, parameter fitting, and Bayesian inference, establishing quantitative biomarkers for early warning signals of dysbiosis.肠道菌群共生稳态向失调状态的转变，是复杂自适应生态系统中一次关键的相变过程，通常以滞后效应与逆转抗性为典型特征。本研究超越描述性框架，提出了一套严谨且可证伪的肠道菌群动力学数学模型。我们将广义洛特卡-沃尔泰拉（Generalized Lotka-Volterra, gLV）方程与反应扩散项相结合，以刻画管腔-黏膜轴线上的空间异质性。此外，我们引入了耦合代谢反馈环路，将短链脂肪酸（Short-Chain Fatty Acid, SCFA）浓度与菌群抗逆性相关联，并显式建模噬菌体-宿主捕食者-猎物动力学，以此作为靶向治疗干预的作用机制。本模型采用源自人类宏基因组数据集（如GMrepo与人类微生物组计划（Human Microbiome Project））的参数进行校准，其中包含炎症性肠病（Inflammatory Bowel Disease, IBD）患者与健康对照人群中有益菌（如普拉梭菌*Faecalibacterium prausnitzii*）与有害菌（如大肠杆菌*Escherichia coli*）的时序丰度数据。我们划定了一套多阶段治疗方案，该方案依托“临界点”概念，提出成功的治疗需推动该生态系统跨越双稳态的分隔边界。本框架提供了可复现的Python代码，用于仿真、参数拟合与贝叶斯推断，同时构建了用于菌群失调早期预警的定量生物标志物。