. 2021 Aug 25;18(181):20210308. doi: 10.1098/rsif.2021.0308

Table 1.

Literature overview. The studies listed in the table were found by a general literature search for mathematical models of antibiotic therapy across a community, including following up on the references and citations of the articles found. We excluded studies that only consider one of the strategies without comparing it with at least one of the others. Best strategy: we list the strategy that emerges as the best one overall. A strategy that still seems to be worth noting based on its performance is added in brackets. When the picture as a whole remains inconclusive but a strategy seems to have some advantage over the others, we note this strategy in brackets.

publication	comparison	optimality criterion	best strategy	R_AB compartment	deterministic/ stochastic	memory	analysis
Bonhoeffer et al. [2]	CYC, MIX, COMB	— no. of uninfecteds in a given time interval	COMB (MIX; CYC)	yes	det.	no	analytical results and computer simulations of a single parameter set
		— no. of uninfecteds until double resistance has reached 50%^a	MIX (CYC, COMB)
		— time until double resistance has reached 50%^a	inconclusive
Bergstrom et al. [3]	CYC, MIX	— average no. of infecteds with res. strain	MIX (CYC)	no	det.	no	parameter sensitivity analysis
Bergstrom et al. [3]	CYC, MIX	— evol. of double resistance via horizontal gene transfer	inconclusive	no	det.	no	parameter sensitivity analysis
Levin & Bonten [4]	CYC, MIX	average no. of infecteds with res. strain	MIX	no	det.	no	computer simulations of individual parameter sets
Beardmore & Peña-Miller [5]	reactive CYC^b, CYC, MIX	— no. of infecteds in a given time interval	reactive CYC	no	det.	no	optimal control theory, computer simulations of a single parameter set
Beardmore & Peña-Miller [5]	reactive CYC^b, CYC, MIX	— no. of infecteds with res. strain	reactive CYC	no	det.	no
Bonhoeffer et al. [6]	reactive CYC, CYC, MIX	— no. of infecteds in a given time interval	MIX	no	det.	no	computer simulations of individual parameter sets
Bonhoeffer et al. [6]	reactive CYC, CYC, MIX	— no. of infecteds with res. strain	MIX	no	det.	no	computer simulations of individual parameter sets
Beardmore & Peña-Miller [7]	CYC, MIX	— no. of infecteds in a given time interval	inconclusive	no	det.	no	analytical considerations, computer simulations of a single parameter set
Beardmore & Peña-Miller [7]	CYC, MIX	— no. of infecteds with res. strain	inconclusive	no	det.	no
Sun et al. [8]	SINGLE, CYC, MIX, COMB	not employed	not discussed	yes	det.	no	analytical treatment of the equilibria
Kouyos et al. [9]	CYC, MIX, ISS^c	— prevalence of resistance	ISS	yes	stoch.	yes	computer simulations of individual parameter sets
Kouyos et al. [9]	CYC, MIX, ISS^c	— no. of inappropriately treated patients	ISS	yes	stoch.	yes	computer simulations of individual parameter sets
Chan et al. [10]	SINGLE, MIX, COMB, THRESH^d, DIFF^e, POC^f	prevalence of infections in time	inconclusive (MIX)	yes	det.	no	computer simulation of a single parameter set
Obolski & Hadany [11]	CYC, MIX, COMB	— evol. of double resistance via mutation	CYC	no	det.	no	moving average over 10⁴ parameter sets
		— no. of infected patients	COMB
		— emergence of double resistance via horizontal gene transfer	CYC (MIX)
Abel zur Wiesch et al. [12]	CYC, MIX	combination of no. of inappropriately treateds and no. of symptomatically infecteds	inconclusive (CYC at optimal frequency)	yes	both	yes	parameter sensitivity analysis
Campbell & Chao [13]	NONE, CYC, ‘MIX’^g, COMB, MONO, CONTROL^h	average no. of uninfecteds in equilibrium	COMB	yes	det.	no	combination of analytical results and computer simulations of individual parameter sets
Xiridou et al. [14]	SINGLE, COMB, THRESH^d	prevalence of infecteds	COMB	yes	det.	no	computer simulation of 1000 parameter sets
Obolski et al. [15]^i,k	SINGLE, CYC, MIX	— mean no. of incorrectly treated patients	MIX	no	det.	no	computer simulation of a single parameter set
Obolski et al. [15]^i,k	SINGLE, CYC, MIX	— evol. of double resistance	inconclusive	no	det.	no	computer simulation of a single parameter set
Beardmore et al. [16]	CYC, MIX, reactive CYC	— no. of infecteds with res. strain	inconclusive (reactive CYC)	no	stoch.	no	conceptual considerations + stochastic computer simulations of individual parameter sets
		— no. of infected patient days	inconclusive (reactive CYC)	no	stoch.	no
		— mean length of hospital stay^j	reactive cycling	NA	stoch.	both versions	individual-based computer simulations of individual parameter set for a nested model of within-host and between-host dynamics
Tepekule et al. [17]	SINGLE, CYC, MIX, COMB, reactive CYC	gain in no. of uninfecteds in 1 year compared with no treatment	COMB (all others)	yes	det.	no	parameter sensitivity analysis
Uecker & Bonhoeffer [18]^k	CYC, MIX	— average no. of uninfecteds	inconclusive	yes	det.	yes	computer simulations of single parameter sets
Uecker & Bonhoeffer [18]^k	CYC, MIX	— spread of double resistance	inconclusive	yes	det.	yes	computer simulations of single parameter sets
Houy & Flaig [19]	COMB, CYC, METRO^l, MONO, THRESH-k^m, INFOBESTⁿ	average cumulative number of infected patient days within 2 yearsⁿ	THRES-1	yes	stoch.	no	averaging over 400 parameter sets

^aThese two criteria have not been systematically studied. ^bReactive cycling denotes a strategy where the default drug is always the one for which resistance is currently less prevalent. For MIX and CYC, drugs can be used unequally (i.e. different proportions in MIX; different periods of use in CYC), and for both strategies the performances under optimal drug use are compared. ^cISS stands for ‘informed switching strategy’. The antibiotic for incoming patients depends on the prevalence of resistance to both drugs in the hospital, and several variants of ISS are tested. The winning strategy is ISS_LAST. In this strategy, the latest time point at which resistance to either drug is detected determines which drug is used. ^dFor THRESH, drug A is used until resistance has reached a threshold. ^eFor DIFF, different strategies are used depending on the risk group, defined through the rate of partner change. ^fFor POC, point-of-care testing is available such that resistant infections can be identified and treated accordingly. ^gMixing is different here since each half of the population cycles the drugs. ^hFor CONTROL, evolution of resistance is impossible (we exclude it from the comparison). ⁱThe main text of the article focuses on the effect of restricted versus an equal use of a third antibiotic. We only consider the briefly investigated two-drug model from electronic supplementary material, supplementary information S3. ^jThe part in italic letters uses an individual-based nested model of within-host and between-host dynamics. ^kThese two studies do not aim to generally assess the performance; we report the results for the examples shown in the articles. ^lMETRO: Combination therapy is alternated with periods of no drug use. ^mTHRES-k: Combination therapy is given if the number of double-resistant infections is below k; otherwise, no drugs are administered. ⁿINFOBEST: The best strategy for a given parameter set. This is by definition the best strategy but requires perfect information regarding the parameters. We exclude it from the comparison.