Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Mathematical Basis for the Assessment of Antibiotic Resistance and Administrative Counter-Strategies

Version 1 : Received: 31 May 2019 / Approved: 3 June 2019 / Online: 3 June 2019 (12:06:31 CEST)
Version 2 : Received: 26 August 2020 / Approved: 27 August 2020 / Online: 27 August 2020 (08:03:07 CEST)

A peer-reviewed article of this Preprint also exists.


Diversity as well as temporal and spatial changes of the proportional abundances of different antibiotics (cycling, mixing or combinations thereof) have been hypothesised to be an effective administrative control strategy in hospitals to reduce the prevalence of antibiotic-resistant pathogens in nosocomial or community-acquired infections. However, a rigorous assessment of the efficacy of these control strategies is lacking. The main purpose here is to present a mathematical framework for the assessment of control stategies from a processual stance. To this end, we adopt diverse measures of heterogeneity and diversity of proportional abundances based on the concept of entropy from other fields and adapt them to the needs in assessing the impact of variations in antibiotic consumption on antibiotic resistance. Thereby, we derive a family of diversity measures whose members exhibit different degrees of complexity. Most important, we extent these measures such that they account for the assessment of temporal changes in heterogeneity including otherwise undetected diversity-invariant permutations of antibiotics consumption and prevalence of resistant pathogens. We apply a correlation analysis for the assessment of associations between changes of heterogeneities on the antibiotics and on the pathogen side. As a showcase, which serves as a proof-of-principle, we apply the derived methods to records of antibiotic consumption and prevalence of antibiotic-resistant germs from University Hospital Dresden. Besides the quantification of heterogeneities of antibiotics consumption and antibiotic resistance, we show that a reduction of prevalence of antibiotic-resistant germs correlates with a temporal change of similarity with respect to the first observation of antibiotics consumption, although heterogeneity remains approximately constant. Although an interventional study is pending, our mathematical framework turns out to be a viable concept for the assessment and optimisation of control strategies intended to reduce antibiotic resistance.


antibiotic cycling; antibiotic mixing; antibiotic resistance; diversity; entropy; heterogeneity


Biology and Life Sciences, Immunology and Microbiology

Comments (1)

Comment 1
Received: 27 August 2020
Commenter: Hans H. Diebner
Commenter's Conflict of Interests: Author
Comment: In this revised version, we clarified the usage of notations like "antibiotic cycling" and "antibiotic mixing" which we used in a somewhat confusing way previously. Moreover, "antibiotic cycling" is often applied in an adjusted rather than a rigorous way in hospitals, leading to "clincal cycling," which matches better with the observation in the analysed dataset. We worked out much more distictly that antibiotic cycling can leave diversity measures of antibiotic consumption invariant but our newly derived differental diversity measure SI_0(t) is capable to address such changes. This point needed to be underpinned as well as our result that SI_0(t) correlates with the corresponding differential diversity of the resistant pathogen prevalences. In addition, SI_0(t) correlates with a decline of prevalence of resistant pathogens. We elaborated on this most important finding since it was too briefly explained in the first version of the preprint. Last but not least, we added an extension (eq. 10) of the diversity measure such that it accounts for mixing. Although mixing was not an issue in our dataset, it is an important part of the mathematical framework which we intented to introduce for general applications to assess the impact of spatio-temporal strategies in antibiotic stewardship. Overall, we restructured the preprint a bit enabling a smoother reading. We also adjusted the abstract slightly to match better with the contents of the full text. Also, we added a few relevant references.
+ Respond to this comment

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 1
Metrics 0

Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.