Hospital Infection Control and Colonization Pressure

Definitions and mathematical statement

The supplied record concerns transmission in hospital wards and names isolation, other control measures, colonization pressure, antibiotic use, rapid molecular tests, and culture-based swabs. It supplies no mathematical definitions of these quantities, no specified pathogen or ward population, and no transmission, observation, or intervention model. In particular, it does not define how colonization pressure is measured or how ward spread and diagnostic usefulness are quantified.

The source-level research questions are:

1. What are the effects of isolation and other control measures on ward spread?
2. How is ward spread related to colonization pressure?
3. What role do antibiotics play?
4. How useful are rapid molecular tests compared with culture-based swabs?

These questions request quantitative understanding, but the supplied record does not specify an estimand, a comparison intervention, a time horizon, or assumptions sufficient to determine a mathematical proposition. A precise quantified statement therefore remains unresolved. In particular, no universal quantification over wards or pathogens, causal interpretation, or functional relationship is imposed by this draft.

Short English statement

Determine the effects of infection-control measures, colonization pressure, and antibiotics on hospital-ward transmission, and compare the usefulness of rapid molecular testing with culture-based swabs. The source leaves the population, model, outcomes, and comparison criteria unspecified, so these remain research questions requiring further formulation.

Sources

• Local UnsolvedMath registry: supplied record with permanent ID $30001366$, title Hospital Infection Control and Colonization Pressure, exact source code catalogue entry, in the Oberwolfach Reports Open Problems collection. The record lists proposed year 2009 and identifies no individual proposer.
• Supplied report citation: Design and Analysis of Infectious Disease Studies (2010), Oberwolfach Reports, pp. 2673--2698, DOI 10.4171/owr/2009/48. https://doi.org/10.4171/owr/2009/48. The supplied background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature source, labeled "original Oberwolfach report 4131": https://doi.org/10.4171/owr/2009/48.
• Supplied literature source, labeled "healthcare infection modelling review": https://pmc.ncbi.nlm.nih.gov/articles/PMC5045168/.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the problem open and states that models and systematic reviews study isolation, colonization pressure, antibiotics, and rapid testing, while reporting no universal answer for all wards and pathogens. This is supplied dated curation, not an independently verified assessment; its time-sensitive status and cited claims require independent verification.
• The registry marks the statement status as "exact" and reports that its mathematical content was checked against the official report, with notation, context, and question form normalized without changing the source-level claim. This verification description is supplied provenance, not verification performed for this draft.