Data-driven epidemiological model.

A) compartments describing host behaviors and sampling. U : individuals who did not travel nor used antibiotics, T : individuals under antibiotic treatment, SEA: individuals traveling to South-East-Asia. the subscript 3 indicates that the corresponding behavior occurred within 3 months before sampling. Only the compartments U, SEA3 and T3 are observed (sampled). B) ESBL frequencies in the three observed host behaviors. C) Structure of the multiple-carriage model. Hosts can be colonized by up to two strains that belong to type C or P (i, j ∈ {C, P}). Estimate of Enterobacterales density in 301 samples allowed to estimate the frequency of uncolonized (thick-open) and mixed-carriage hosts (thick-red). Solid, dashed and dotted arrows represent colonization, natural clearance and antibiotic-driven clearance, respectively. D) Density of ESBL-carrying Enterobacterales as a function of the total density of Enterobacterales. Dark square: all Enterobacterales in the sample carried ESBL (R carriage hosts); red-filled dots: mixed-carriage (RS) hosts. Solid, dashed and dotted lines: fraction of ESBL-carrying strains equals 100%, 10% and 1% of the total.

Parameters of the model.

Parameters to be inferred (in the set PR) are in italic. In the column “Value”, bracket intervals denote the ranges investigated. We used uniform prior within these ranges for the parameters in PR. Hyphens indicate that the value of the parameters is defined by the value of the δ’s. Rate parameters are in units of months−1. See also Supp.Mat. S3

ESBL carriage as a function of time.

Black: ESBL frequency in the community, measured from French children during the period 2010-2018 (focal data set). Blue: ESBL frequency in outpatients in data from the European Center for Diseases prevention and Control (ECDC), available for outpatients only over the period 2002-2010. Data are mean percentages with 95% confidence intervals. The thin gray line is a logistic model with a plateau fitted to these data with least squares, with weights proportional to the number of isolates at each timepoint. The gray envelope shows the 95% confidence intervals.

Posterior distribution of the five estimated parameters.

For all panels : Colored curves : posterior distribution for each of the five MCMC chains. Black curve: all chains pooled. Vertical line: Mean of the distribution. Shaded area: 95% CI. A and B, costs of resistance on colonization of uncolonized δβ,R,1 and single-colonized hosts δβ,R,2, respectively. C and D, additional clearance of resistant strains from single colonized δγ,R,1 and co-colonized hosts δγ,R,2, respectively. E: mx. costs of resistance on colonization and clearance. The prior distributions of all parameters are uniform on the intervals [0,1], [0,1], [0,10], [0,10], and [0,1], respectively.

Sensitivity of the frequency of resistance to the rates of treatment, transmission and travel.

A, the frequency of resistance as a function of the treatment rate, shown for four values of the travel rate. The dashed vertical line is the reference value. The inset shows the logit-transformed resistance frequency (log10(pR/(1 − pR)) specifically in the low-treatment region, highlighting the impact of travel in these conditions. B, the frequency of resistance as a function of the relative transmission rate, for three values of the treatment rate. On panels A & B, the arrows highlight the effect of a change in treatment rate or transmission on resistance frequency. C, D contour plots of the frequency of resistance as a function of treatment, transmission and travel rate. The points show the reference values. When unspecified, parameters are fixed to their reference value as given in Table 1.

Effect of the treatment rate (A), travel rate (B) and transmission rate (C) on frequency-dependent selection on resistance.

Frequency-dependent selection is shown by the selection coefficient on resistance as a function of resistance frequency. The selection coefficient is measured as sR = d/dt(log(pR/(1 − pR)).

Effect of niche differentiation along the colonization-persistence trade-off on negative-frequency-dependent selection (NFDS).

Frequency-dependent selection is shown by the slope of the selection coefficient on resistance as a function of resistance frequency. A: Comparison of NFDS produced by the (main) model with both a colonizer and a persistent strategy and that of a model with a single generalist strategy with the same fitness. In the generalist model, resistance costs (PR) were inferred similarly to the main model. B: Association of resistance with the persistent strategy in a model assuming differentiated strategies along the persistent/colonization trade-off. The association is measured as the proportion of RP−carrying hosts among all R-carrying hosts. Differentiation d is measured as departure from the mean strategy: and for the colonizer and opposite (− d) for the persistent. Other parameters as in Table 1.

Contingency table for the number of occurrences of each risk factor considered in the model

Analysis of risk factors associated with ESBL carriage (extended from Birgy et al. 2016 to the period 2010-2018); overall samples N = 3443, carriage of ESBL = 257 (7.4%).

The univariate analysis was performed using χ-square tests. For the multivariate analysis, we kept only the most significant factors of the univariate analyses (P<0.2). Children who did not travel were pooled with those who travelled to western/northern Europe. In the multivariate analysis, we considered only the children with information on travel history (2012-2018).

Distribution of the relative ESBL density

Sample size adjusted for the autocorrelation (rounded to the nearest integer)

Gelman and Rubin’s convergence diagnostic (implemented in R-package coda)

Gelman-Rubin convergence plots.

A: mx, B: δβ,R,1, C: δβ,R,2, D: δγ,R,1, E: δγ,R,2

Posterior distribution under the assumption of strong competitive release during treatment.

For all panels: colored curves represent the posterior distribution for each MCMC chain. The thick black curves is the posterior for all chains pooled. The vertical lines are the mean of the overall posterior distribution. Shaded area: 95% CI.

Posterior distribution under the assumption of density independent transmission and clearance rates.

For all panels: colored curves represent the posterior distribution for each MCMC chain. The thick black curves is the posterior for all chains pooled. The vertical lines are the mean of the overall posterior distribution. Shaded area: 95% CI.

Posterior distributions after inference for the two strain model.

Setting and parameters similar to Fig. 3.

Sensitivity of the frequency of resistance to the treatment rate in the community predicted by the four-strain model (dark red, including genetic structuring as in main text) and the two-strain model (dark blue, without genetic structuring).

All other parameters as in Table 1 and mean inferred values from the posterior distributions.

Dynamics of R frequency predicted by the two-strain and four-strain model and comparison with observed dynamics (as in Fig. 2).

Red: four-strain model with genetic structuring (main text). Pink: two-strain model (without genetic structuring).

Strain dynamics following the introduction of resistance by travelers at t = 0.

A: sensitive strains. B: resistant strains. Same parameters as in Table 1.

Correlation plot for the parameters in P when all MCMC chains are pooled.

Goodness of fit of the model.

Histograms show the distribution of the frequencies of each type of hosts predicted by the model. The dashed-red vertical line show the frequencies of each type of hosts observed in the data set. The solid lines show the 95% CI for the observed frequencies, assuming that the count for each type of hosts is drawn in a binomial distribution B(n,p) with n = number of the corresponding type of host observed and p = the observed frequency of the host type.

Frequency of ESBL as a function of age in E. coli infections in European hospitals.

We used data from the ECDC on the frequency of resistance to in E. coli isolates in invasive infections (blood, cerebrospinal fluid). We fitted to these data a logistic model for resistance status as a function of year as factor, type of patient (inpatient or outpatient), and age category. We show the predicted resistance for an inpatient infected in 2019, as a function of age category, with 95% confidence intervals. The dashed line is for the [0-4] age category.