AI 中文总结
本研究针对细菌感染的基于智能体模型推导确定性粗粒化描述，构建半离散及状态结构化反应-扩散系统，数值验证其与集成平均ABM模拟吻合，所得模型更便于大规模模拟与参数研究。
AI 中文摘要
基于智能体的模型（ABMs）为表征细菌感染中的细胞层面规则与空间异质性提供了自然框架，但其计算成本限制了其在宏观组织尺度模拟及广泛参数探索中的应用。我们针对一类细菌感染ABMs推导了确定性粗粒化描述，该模型中免疫细胞与胞外细菌发生扩散，免疫细胞吞噬邻近细菌，胞内细菌载量通过规定的增殖与清除过程演化。首个粗粒化模型为半离散反应-扩散系统，其保留了每个免疫细胞细菌载量的离散内部状态，同时以连续浓度场表征细胞与细菌种群。关键技术步骤是从微观ABM参数推导依赖状态的有效吞噬率：通过求解单个细菌周围的辅助扩散问题，计算免疫细胞进入相互作用区域的通量得到这些速率。随后我们对内部状态变量取连续极限，得到一个状态结构化的反应-扩散系统，其中胞内动力学表现为状态空间中的平流与扩散。与集成平均ABM模拟的数值比较显示，在符合生物学意义的参数范围内二者吻合度高。所得框架保留了ABM基于规则的结构，同时生成的偏微分方程模型对于大规模模拟和参数研究而言显著更易处理。
英文摘要
Agent-based models (ABMs) provide a natural framework for representing cell-level rules and spatial heterogeneity in bacterial infections, but their computational cost limits their use for macroscopic tissue-scale simulations and broad parameter exploration. We derive a deterministic coarse-grained description for a class of bacterial-infection ABMs in which immune cells and extracellular bacteria diffuse, immune cells ingest nearby bacteria, and intracellular bacterial loads evolve through prescribed birth and clearance processes. The first coarse-grained model is a semidiscrete reaction--diffusion system that retains a discrete internal state for each immune-cell bacterial load while representing cell and bacterial populations by continuum concentration fields. The key technical step is the derivation of state-dependent effective ingestion rates from the microscopic ABM parameters: these rates are obtained by solving an auxiliary diffusion problem around a single bacterium and computing the flux of immune cells into the interaction region. We then take a continuum limit in the internal state variable, yielding a state-structured reaction--diffusion system in which intracellular dynamics appear as advection and diffusion in state space. Numerical comparisons with ensemble-averaged ABM simulations show close agreement in biologically motivated parameter regimes. The resulting framework preserves the rule-based structure of the ABM while producing PDE models that are substantially more tractable for large-scale simulation and parameter studies.
Comments30 pages, 8 figures
