Antibiotic Resistance Persistence in Companion Animal Models

Definitions and mathematical statement

The three bacterial classes named in the supplied record are wild-type bacteria, bacteria with mutation-mediated antibiotic resistance, and bacteria with plasmid-mediated antibiotic resistance, within a domestic pet (companion animal). The record does not specify whether the resistant classes are mutually exclusive, whether bacteria can possess both resistance mechanisms, or how the classes interact.

Requested problem. For the within-host model intended by the source, determine whether its dynamics predict that a companion animal can become a source of antibiotic resistance, and characterize the parameter regimes under which the bacterial strains persist or coexist.

Unresolved mathematical specification. The supplied record does not give the model equations or transition rules, state space, parameter domains, initial conditions, boundary conditions, or antibiotic-exposure assumptions. It also does not define "source of antibiotic resistance," "persistence," or "coexistence." In particular, it does not specify whether persistence and coexistence concern positive equilibria, long-term survival along particular trajectories, uniform persistence over a class of initial states, or a stochastic survival criterion. Nor does it specify whether being a source requires within-host production or maintenance of resistance, shedding, or transmission to another host. These alternatives are not interchangeable. No particular interpretation or quantifier over parameters and initial states is selected here. Consequently, the requested task is preserved, but a uniquely specified mathematical proposition cannot be recovered from the supplied record alone.

Short English statement

Determine when the intended within-host model predicts that a pet maintains or supplies antibiotic resistance, and when its wild-type, mutation-resistant, and plasmid-resistant bacterial strains persist or coexist. The model and the meanings of these outcomes are missing, so this remains an incomplete problem specification requiring source clarification and human mathematical review.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30003732$, source problem code catalogue entry, title: Antibiotic Resistance Persistence in Companion Animal Models. The project identifies data/unsolvedmath/problems.json and catalog/problems.json as registry resources; their contents have not been independently inspected for this draft. No individual proposer is identified in the supplied record.
• Supplied source citation: Design and Analysis of Infectious Disease Studies (2019), Oberwolfach Reports, pp. 383--432, DOI 10.4171/owr/2018/7. https://doi.org/10.4171/owr/2018/7. The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions. The record gives proposed year 2018; the relationship between that year and the citation's 2019 date is not explained.
• Supplied literature reference, "original OWR report": https://doi.org/10.4171/OWR/2018/7.
• Supplied literature reference, "Park, resistant E. coli in pet-owner households": https://doi.org/10.1292/jvms.16-0585.
• Supplied literature reference, "Caddey et al., companion-animal AMR transmission review": https://doi.org/10.1128/cmr.00146-22.
• Literature assessment dated 2026-08-21: the supplied curation labels the problem partially solved and states that companion animals can carry and share antimicrobial-resistant organisms with humans, including resistant E. coli, while the frequency and direction of transmission in ordinary households remain incompletely determined. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment or a mathematical conclusion established in this draft. The source explicitly requests independent verification of time-sensitive status and cited claims.
• The registry labels the statement corrected_verified and says that mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. These are supplied editorial assertions; they do not supply the missing model or establish mathematical correctness.