Analysis of persistence thresholds for a nonlocal PDE--ODE model of bacterial persister cells
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910179208986624 |
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| author | Li, Chongming Meadows, Tyler Day, Troy |
| author_facet | Li, Chongming Meadows, Tyler Day, Troy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18809 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analysis of persistence thresholds for a nonlocal PDE--ODE model of bacterial persister cells Li, Chongming Meadows, Tyler Day, Troy Analysis of PDEs Populations and Evolution 35K57, 92D25, 47D06, 35R09 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. |
| title | Analysis of persistence thresholds for a nonlocal PDE--ODE model of bacterial persister cells |
| topic | Analysis of PDEs Populations and Evolution 35K57, 92D25, 47D06, 35R09 |
| url | https://arxiv.org/abs/2604.18809 |