Coarse-Graining Agent-Based Models of Bacterial Infections

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.

Source: arXiv:2609.03212v1 - http://arxiv.org/abs/2609.03212v1 PDF: https://arxiv.org/pdf/2609.03212v1 Original Link: http://arxiv.org/abs/2609.03212v1