Analysis of persistence thresholds for a nonlocal PDE--ODE model of bacterial persister cells

Li, C.; Meadows, T.; Day, T.

doi:10.64898/2026.04.20.719571

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bioRxiv · 10.64898/2026.04.20.719571

Analysis of persistence thresholds for a nonlocal PDE--ODE model of bacterial persister cells

Li, C.·Meadows, T.·Day, T.

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Abstract

Within many bacterial colonies, persister cells exist as a subpopulation that is tolerant to antibiotics and other stressors, yet not genetically distinct from the rest of the colony. A recent study has proposed epigenetic inheritance as a mechanism that leads to the presence of persister cells. We analyze a nonlocal PDE-ODE model introduced in that study to describe the epigenetic inheritance process and establish its mathematical well-posedness, including existence, uniqueness, and nonnegativity of solutions. We identify a sharp parameter threshold delineating extinction from persistence of the colony: below this threshold the washout equilibrium is globally asymptotically stable, while above it a unique positive equilibrium exists and the population is weakly persistent. Notably, this threshold is independent of the internal community structure.

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Li, C., Meadows, T., Day, T.. 2026-04-22. Analysis of persistence thresholds for a nonlocal PDE--ODE model of bacterial persister cells. https://doi.org/10.64898/2026.04.20.719571

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