Modeling the Transmission of ESBL and AmpC-Producing Escherichia coli in Denmark: A Compartmental and Source Attribution Approach

Simple Summary

Antimicrobial resistance is a huge concern for public health. Escherichia coli causes a variety of infections and is often associated with resistance to a broad range of antibiotics. This study investigates how antibiotic-resistant E. coli spreads among people, animals, and food sources in Denmark. We used different types of models to study transmission patterns in farmers, pet owners, and the general population and analyzed how different sources, like imported food, livestock, and pets, contribute to the spread. By identifying key transmission sources and pathways, this study supports more effective strategies to control the spread of resistant E. coli. It also underscores the need for a One Health approach that addresses human, animal, and environmental health together.

Abstract

Extended-spectrum cephalosporin-resistant Escherichia coli (ESC-EC) poses a significant public health concern, with its presence increasingly detected in healthy humans and various animal species. This study explores the transmission dynamic of ESC-EC within the Danish population as well as the transmission impact of a range of food and animal sources. We developed a compartmental model encompassing farmers, pet owners, and the general population. Additionally, we applied an established source attribution model to estimate the contributions to the transmission of different sources using Danish surveillance data on the distribution of resistance genes in E. coli. Our findings highlight the central role of human-to-human transmission while also showing the significant contributions of food and animal sources to the spread of ESC-EC in sporadic human infections. Imported food, pets, and livestock were estimated to contribute importantly to human infections. The results emphasize the complexity of ESC-EC transmission dynamics and the critical value of employing a One Health approach in modeling disease transmission and in the development of targeted intervention strategies.

1. Introduction

Antimicrobial resistance (AMR) has been a concern since the discovery of antibiotics, but it has progressively escalated into a global crisis, contributing to an estimated 1.27 million deaths annually [1]. Escherichia coli is among the leading pathogens associated with resistance, particularly due to the production of extended-spectrum beta-lactamases (ESBLs) and plasmid-mediated AmpCs (pAmpCs), which confer resistance to a broad range of beta-lactam antibiotics, including penicillins and cephalosporins [2]. These strains, referred to as extended-spectrum cephalosporin-resistant E. coli (ESC-EC), are increasingly being detected not only in healthcare settings but also in the broader community [3]. Infections caused by ESC-EC often lead to prolonged or recurring, potentially life-threatening, infections due to therapeutic failures.

ESC-EC has become increasingly prevalent in livestock, which are recognized as reservoirs for these resistant bacteria. Since 2014, ESC-EC in livestock has been monitored and reported under European legislation [4]. This has led to a growing focus on ESC-EC from a One Health perspective, emphasizing the interconnectedness of human, animal, and environmental health in the transmission of resistance. This focus has resulted in the expanded collection of ESC-EC isolates not only from humans and livestock but also from other animals and environmental sources, such as vegetables [5,6]. However, the transmission dynamics of resistance between animals and humans and the understanding of the impact of different sources on human exposure are not well understood [7,8].

National source attribution models, such as those developed for Germany and the Netherlands, have compared the genotype and phenotype distribution of ESC-EC between human and animal sources [9,10]. These models found that human-to-human transmission is the main route for asymptomatic carriage in humans but also highlight the importance of non-human sources and the complexity of the transmission dynamics. Various approaches have been employed to understand the transmission dynamics of ESC-EC better. These include comparative exposure assessments, genomic relatedness studies, and time-discrete models [5,11,12].

In Denmark, ESC-EC data are collected through the Danish Integrated Antimicrobial Resistance Monitoring and Research Programme (DANMAP), which annually monitors antimicrobial use and resistance in animals and humans [13]. Recent DANMAP reports show that E. coli is the most frequent cause of community- and hospital-acquired bacteremia and urinary tract infections in Denmark. While the proportion of ampicillin-resistant isolates has slightly decreased, the total number of cases has risen markedly, with a 143% increase in ESC-EC isolates from urinary samples in primary healthcare between 2013 and 2023 [14].

Genomic comparisons of ESC-EC from Danish human bloodstream infections and livestock showed findings that are consistent with studies from Germany and the Netherlands. However, the sources were limited to livestock and did not include isolates from healthy carriers in the broader community or in companion animals, both of which may play a role in the transmission [9,10,14,15].

Given the complex transmission pathways and the involvement of multiple sources, modeling approaches that account for different population groups is necessary to better understand the transmission dynamics. Compartmental models can be especially useful for investigating the transmission of disease within sub-populations, also allowing for the exploration of the increased risk of an ESC-EC infection associated with antibiotic use.

This study aims to explore ESC-EC transmission within the Danish population by developing a compartmental model to simulate the transmission dynamics across various sub-populations while accounting for antibiotic use. Additionally, an established source attribution model was applied to quantify the relative contribution of different sources—such as livestock, companion animals, and humans—to ESC-EC carriage or infections using the distribution of resistance genes in ESC-EC from surveillance data representative of Denmark.

2. Materials and Methods

This population-based modeling study compares two different modeling approaches: a compartmental model and a source attribution model. The models are based on data from the DANMAP report collected between 2018 and 2022 [16]. The models aim to assess the contribution of various sources to the spread of ESC-EC in sporadic infections, including domestic food and food-producing animals (broilers, cattle, and pigs), imported food (from broilers, cattle, pigs, and turkeys), and companion animals (cats, dogs, and horses).

2.1. Compartmental Model of the General Population, Farmers, and Pet Owners

To simulate the spread of ESC-EC in the Danish population, we developed a compartmental model with four main epidemiological stages: susceptible, colonized, infected, and infected receiving antibiotics (S, C, I, and I_A, respectively). The structure of the model is illustrated in Figure 1, with detailed equations provided in the Supplementary Materials (Equations). Transmission pathways included human-to-human interactions, foodborne transmission, travel-related colonization, and direct contact with animals (e.g., livestock and pets).

The Danish population was divided into three subpopulations to account for different transmission patterns: the general population, farmers, and pet owners. The model features an open population structure for the general population and pet owners, while farmers are modeled as a closed population due to their small proportion of the total population. To simplify the model, farmers were therefore assumed not to be pet owners.

In each subpopulation, susceptible individuals can become colonized with ESC-EC through either human-to-human transmission or foodborne exposure, denoted by the rates ${\beta }_h$ and ${\beta }_f$. Travel-related colonization is modeled within the general population to account for the increased risk of ESC-EC carriage ($\lambda$) [17,18,19]. Animal-related transmission is incorporated through contact with pets (${\beta }_p$) and livestock (${\beta }_l$), applied to pet owners and farmers, respectively. Transmission rates for food, livestock, and pets are modified by probabilities of transmission at the point of exposure (${\eta }_f$, ${\eta }_l$, and ${\eta }_p$) that account for risk reduction due to interventions like cooking or hygiene practices. The disease progression—decolonization, infection, and recovery—follows the same structure across all subpopulations.

Previous studies have shown that individuals treated with antibiotics within 30 days prior to infection have a significantly higher risk of infection (an odds ratio of 3.7 [20]) but no increased risk of colonization [21]. To capture this dynamic, the colonized can progress to infection or infection receiving antibiotics. To split the progression of disease, the rate of antibiotic exposure ($\rho$) and the subsequent increased risk ($\theta$) are incorporated into the model. While individuals remain within their respective subpopulations, transmission of ESC-EC between subpopulations is possible, occurring at rates ${\omega }_G$ (general population), ${\omega }_F$ (farmers), and ${\omega }_P$ (pet owners). These rates are recalculated at each time step, assuming equal infectivity for colonized and infected individuals [22].

The model simulates a five-year period, with the first two years as a burn-in phase to ensure reliability and stability for the initial stage. To estimate the contribution of each animal and food source to the overall infection rate, we ran the simulation while removing one source at a time. The total number of infections in the final year was recalculated for each model simulation. The parameters used in the model were either based on estimates from the literature or estimated as part of the model optimization (Table 1). ${\beta }_h$, ${\eta }_f$, ${\eta }_p$, ${\eta }_l$, and $\delta$ were estimated by minimizing the normalized sum of squared errors. These errors were calculated as the difference between the modeled number of colonized people and the target colonization prevalence values for the general population (3.7%) [23,24], farmers (11.0%) [25,26,27,28,29], and pet owners (4.2%) [30,31,32].

To identify which parameters impact disease spread the most, we conducted a sensitivity analysis across all subpopulations. Partial rank correlation coefficients (PRCCs) were calculated to assess the impact of each parameter on colonization rates [33].

Table 1. Input parameters used in the baseline model.

Parameter	Description	Value	Source
$N$	Total size of the Danish population at the beginning of the model period	5.97 × 106	[34]
$N_G$	Size of the population in the general population at the beginning of the model period	3.92 × 106	$N-N_F-N_P$
$N_F$	Size of the population that is farmers (broilers, cattle, or pigs)	2.49 × 104	[35]
$N_P$	Size of the population that has pets (cat, dog, or horse) at the beginning of the model period	2.02 × 106	[36]
${\beta }_h$	Human-to-human transmission	2.51 × 10−3/day	Estimated
${\beta }_f$	Total transmission rate for food	4.08 × 10−3/day	Table S1 [16,37,38,39,40,41]
${\beta }_p$	Total transmission rate for pets (cat, dog, and horse)	6.27 × 10−2/day	Table S1 [36,42,43,44]
${\beta }_l$	Total transmission rate from livestock	2.03 × 10−2/day	Table S1 [16,35,41,45]
$\lambda$	Rate of colonized travelers	2.64 × 10−5/day	Table S1 [18,46,47,48]
${\eta }_f$	Probability of exposure to food	1.89 × 10−2/day	Estimated
${\eta }_p$	Probability of exposure to pets	1.83 × 10−3/day	Estimated
${\eta }_l$	Probability of exposure to livestock	8.13 × 10−2/day	Estimated
$\alpha$	Rate of infection	6.91 × 10−4/day	Table S1
$\rho$	Rate of antibiotic exposure	2.43 × 10−5/day	Table S1
θ	Increased risk of infection while on antibiotics	3.7	[20]
$\delta$	Rate of infected individuals initiating antibiotic therapy	9.00 × 10−2/day	Assumed
$\gamma$	Recovery rate	2.60 × 10−3/day	[49]
${\gamma }_A$	Recovery rate in case of antibiotic usage	4.76 × 10−2/day	Assumed
$\sigma$	Decolonization rate	1.75 × 10−2/day	Estimated
${\omega }_G$, ${\omega }_F$, ${\omega }_P$	Disease transmission between groups	-	Supplementary S1
${\upsilon }_G$, ${\nu }_P$	Birth rates	${\upsilon }_G=$ 1.04 × 102/day ${\upsilon }_P=$ 5.34 × 101/day	[50]
${\mu }_G$, ${\mu }_P$	Natural death rates	${\mu }_G=$ 2.22 × 10−5/day ${\mu }_P=$ 1.14 × 10−5/day	[51]

Table 1. Input parameters used in the baseline model.

Parameter	Description	Value	Source
$N$	Total size of the Danish population at the beginning of the model period	5.97 × 106	[34]
$N_G$	Size of the population in the general population at the beginning of the model period	3.92 × 106	$N-N_F-N_P$
$N_F$	Size of the population that is farmers (broilers, cattle, or pigs)	2.49 × 104	[35]
$N_P$	Size of the population that has pets (cat, dog, or horse) at the beginning of the model period	2.02 × 106	[36]
${\beta }_h$	Human-to-human transmission	2.51 × 10−3/day	Estimated
${\beta }_f$	Total transmission rate for food	4.08 × 10−3/day	Table S1 [16,37,38,39,40,41]
${\beta }_p$	Total transmission rate for pets (cat, dog, and horse)	6.27 × 10−2/day	Table S1 [36,42,43,44]
${\beta }_l$	Total transmission rate from livestock	2.03 × 10−2/day	Table S1 [16,35,41,45]
$\lambda$	Rate of colonized travelers	2.64 × 10−5/day	Table S1 [18,46,47,48]
${\eta }_f$	Probability of exposure to food	1.89 × 10−2/day	Estimated
${\eta }_p$	Probability of exposure to pets	1.83 × 10−3/day	Estimated
${\eta }_l$	Probability of exposure to livestock	8.13 × 10−2/day	Estimated
$\alpha$	Rate of infection	6.91 × 10−4/day	Table S1
$\rho$	Rate of antibiotic exposure	2.43 × 10−5/day	Table S1
θ	Increased risk of infection while on antibiotics	3.7	[20]
$\delta$	Rate of infected individuals initiating antibiotic therapy	9.00 × 10−2/day	Assumed
$\gamma$	Recovery rate	2.60 × 10−3/day	[49]
${\gamma }_A$	Recovery rate in case of antibiotic usage	4.76 × 10−2/day	Assumed
$\sigma$	Decolonization rate	1.75 × 10−2/day	Estimated
${\omega }_G$, ${\omega }_F$, ${\omega }_P$	Disease transmission between groups	-	Supplementary S1
${\upsilon }_G$, ${\nu }_P$	Birth rates	${\upsilon }_G=$ 1.04 × 102/day ${\upsilon }_P=$ 5.34 × 101/day	[50]
${\mu }_G$, ${\mu }_P$	Natural death rates	${\mu }_G=$ 2.22 × 10−5/day ${\mu }_P=$ 1.14 × 10−5/day	[51]

2.2. Source Attribution Model Based on Resistance Genes

The ESC-EC isolates used for source attribution originated from healthy production animals and food products (broilers, cattle, pigs, and turkeys), clinical cases in companion animals (cats, dogs, and horses), and clinical cases and healthy carriers in the human population.

Danish livestock and human isolates from bloodstream infections were collected between 2015 and 2022 as part of the Danish surveillance system DANMAP [16]. Additionally, human clinical isolates were obtained from the “One Day in Denmark” project collected in 2018 [52,53]. To include healthy individuals colonized with ESC-EC, data were gathered from Swedish and Norwegian studies, as Danish isolates were not available [23,24]. Isolates from companion animals were obtained from the Swedish Swedres-Svarm reports [54], collected from cases visiting veterinary clinics between 2008 and 2022. Isolates with the TEM-1 gene only were excluded from the modeling, as some TEM-1 variants usually do not confer extended-spectrum resistance [55].

We utilized a variation of the commonly applied Bayesian source attribution model developed for Salmonella [56]. This method has been adapted for Campylobacter, Listeria, and ESC-EC [9,10,57,58]. The principle is to compare the distribution of pathogen subtypes, in this case resistance genes, in isolates from humans with those from different reservoirs, including animals and food sources. Isolates from livestock and food sources are grouped under the same reservoir, e.g., cattle and beef, broilers and chicken meat, and pigs and pork.

The model estimates the number of human cases attributable to each source j using the following equation:

$$o_i~poisson\left({\sum }_j{\lambda }_{ij}\right)$$

(1)

Here, $o_i$ represents the observed frequency of resistance gene i in human cases, and ${\lambda }_{ij}$ is the expected frequency of gene i from source j, calculated as:

$${\lambda }_{ij}=p_{ij}\ast q_i\ast a_j$$

(2)

where $p_{ij}$ is the prevalence of gene i in source j, calculated as ${\mathsf{\pi }}_j\ast {\mathrm{r}}_{ij}$ with ${\mathsf{\pi }}_j$ being the overall prevalence of ESC-EC in source j and ${\mathrm{r}}_{ij}$ being the relative frequency of gene i in source j (Table S2). $q_i$ is an unknown gene-dependent factor, and $a_j$ is an unknown source-dependent factor. $q_i$ and $a_j$ are estimated by the model using uninformative priors. For a detailed description of the parameters used in the model, see Table S3.

Since ESC-EC transmission occurs between humans, we applied the source attribution model in two ways: (1) to human clinical cases (denoted as the “infected model”), where colonized people in the general population were considered a potential source, and (2) to colonized individuals in the general population, where clinical cases were modeled as a potential source (the “colonized model”).

The source attribution models were implemented using the rjags package [59] in the R software (version 2024.04.2+764). Three independent Markov chains were run for 100,000 sampling iterations, with a burn-in period of 30,000 iterations. To control computational efficiency and reduce sample autocorrelation, thinning was applied, retaining every tenth sample and discarding the rest. We identified resistance genes present in human and non-human isolates. Isolates with shared resistance genes between clinical human cases (infected) and source isolates or between colonized humans and source isolates were included in the analysis. Genes only present in source isolates were included to keep the within-source gene relative frequencies in the models.

3. Results

3.1. Compartmental Model

The compartmental model simulated the transmission dynamics of ESC-EC across three key population groups: the general population, farmers, and pet owners in the Danish population.

We estimated five parameters to reach the target prevalences of ESC-EC colonization in each subpopulation. In the final simulated year, we assessed the number of individuals who were colonized, infected, and infected while on antibiotics within each population group (

Table 2. Number of colonized, infected, and infected on antibiotics in the last year of simulation.

	Colonized	Infected	Infected on Antibiotics
General population	925,015	37,365	1198
Pet owners	544,307	21,098	705
Farmers	17,369	678	23
Total	1,486,691	59,141	1926

). In the final year, the model predicted 61,067 infected individuals, aligning with epidemiological data from Denmark. Of these, 1926 (3.2%) infections occurred in individuals on antibiotics, with the majority in the general population (n = 1198), followed by pet owners (n = 705) and farmers (n = 23). By contrast, infections unrelated to antibiotic use were more common, totaling 59,141 cases. The general population accounted for 37,365 cases, while pet owners and farmers accounted for 21,098 and 678 infections, respectively.

As shown in Figure 2, human transmission significantly impacted the total number of infections in the final year of the simulation, leading to a 79% reduction. Removing all livestock was the second-most influential factor overall, resulting in a 48% reduction when excluded. Cattle had the most considerable effect among specific livestock sources, reducing infections by 27% when removed. Food-related transmission collectively accounted for a 17% reduction in infections; however, its impact was smaller than human transmission and cattle from livestock. Within the food category, the contribution of pigs varied from chicken and cattle, as pigs were the highest contributor. Generally, imported meat had a higher impact on infection rates than domestic meat. By contrast, removing pets resulted in a 9% reduction in infections, while excluding colonized returning travelers had a minimal effect, leading to only a 3% reduction.

According to the partial rank correlation coefficient (PRCC) analysis (Figure S1), the decolonization rate showed the highest negative correlation with colonization among the three subpopulations. In the general population, the highest positive correlation with colonization was observed for human-to-human transmission (0.95), livestock transmission, and the probability of transmission from livestock (e.g., the risk reduction due to hygiene practices), with a correlation coefficient of 0.71. For farmers, colonization was strongly correlated with the transmission rate and transmission probability from livestock. On the other hand, pet owners did not exhibit a comparable strong correlation between colonization and pet transmission, indicating that transmission from pets is not a major factor in this population.

3.2. Gene-Specific Source Attribution Model

A total of 2696 isolates from two human and ten non-human sources were identified for use in the source attribution models. The dataset included 1295 isolates from clinical cases, 265 from healthy colonized humans, and 1136 from various animal sources. Across these isolates, 101 distinct resistance-gene combinations were identified: 40 isolates contained a single gene, 48 had two genes, and 13 had three or more genes. The most commonly found gene was CTX-M-15, present in 772 isolates, 691 of which contained only this gene. TEM-1 and CTX-M-1 were the second- and third-most frequently identified genes, found in 366 and 365 isolates, respectively. Notably, TEM-1 variants were often present in combinations with other resistance genes. Fifty-five of the gene combinations were found in only a single isolate. Of the 101 gene combinations, only 20 were identified in both colonized humans and the respective sources and used in the “colonized model”. For the “infected model”, 21 gene combinations were used.

Imported turkey meat and dogs were estimated as the primary source for the “colonized model” and “infected model”, respectively, with attribution percentages of 33.3% and 20.3% (

Table 3. Estimated number of individuals colonized with ESC-EC attributed to sources included in the “colonized model”.

Source	Mean (95% CI)	Median	SD	Percent
Turkey import	95.3 (52.7–145.4)	93.8	23.7	33.3
Human Infected	85.6 (33.2–138.1)	85.7	27.3	29.9
Pig import	19.8 (4.4–43.5)	18.3	10.3	6.9
Dog	17.5 (1.2–47.8)	15.1	12.3	6.1
Cat	9.2 (0.2–35.1)	6.2	9.5	3.2
Horse	7.4 (0.3–22.1)	6	6	2.6
Cattle	7.3 (0.7–22.5)	5.8	5.8	2.6
Cattle import	6.5 (1.2–17.1)	5.6	4.2	2.3
Broilers import	6.2 (0.2–19.3)	4.9	5.2	2.2
Pig	4.8 (1.4–10.3)	4.4	2.3	1.7
Broilers	0.7 (0–2.2)	0.5	0.6	0.2
Not predicted	25.8			9.0

and

Table 4. Estimated number of individuals infected with ESC-EC attributed to sources included in the “infected model”.

Source	Mean (95% CI)	Median	SD	Percent
Dog	262.9 (50.5–566.3)	244.8	137.1	20.3
Turkey import	242.0 (11.4–587.4)	220.6	161.6	18.7
Human colonized	206.6 (48.1–448.4)	191.6	104.9	16.0
Cat	106.5 (2.5–380.1)	74.2	102.4	8.2
Pig import	58.0 (1.9–183.2)	45.2	49.5	4.5
Horse	41.4 (1.3–130.7)	32.5	35.1	3.2
Cattle import	38.5 (1.2–98.1)	21.4	25.8	2.2
Broilers import	24.2 (1.0–75.5)	19.4	20.1	1.9
Cattle	21.7 (0.8–73.8)	16.2	19.7	1.7
Pig	5.1 (0.2–15.6)	4.1	4.2	0.4
Broilers	2.1 (0.1–6.7)	1.6	1.8	0.2
Not predicted	295.7			22.8

). In the “colonized model”, infected humans were the second-most important source, contributing 32.2%. Gene-specific attribution (Figure 3) revealed that some gene combinations were exclusive to a single source, such as CTX-M-8, CTX-M-27.TEM-1, CTX-M-15.OXA-1.TEM-1, and CTX-M-101. CTX-M-9 was attributed to multiple sources, but all were within pets. In general, infected humans (green) and imported meat (shades of purple) were the sources contributing the most to colonized humans. The model could not attribute 9% of the isolates to any source.

In the “infected model”, dogs were followed by imported turkey meat (18.7%) and colonized humans (16.0%) as the most contributing sources. The model could not attribute 22.8% of the isolates to any included sources. Gene-specific attribution (Figure 4) showed generally higher probabilities for pets (blue shades) and imported meat sources (purple shades). For example, CMY-4 was exclusively attributed to dogs. Among infected humans, AmpC was the only gene combination showing a high probability of originating from domestic animal sources, with pigs having the highest relative probability. CTX-M-101 and CTX-M-27.TEM-1 were the only gene combinations found in colonized and infected humans but absent from non-human sources.

4. Discussion

This study has developed two distinct models to model and investigate the sporadic transmission dynamics of ESBL/pAmpC-producing E. coli (ESC-EC) in the Danish population, focusing on contributions from various food and animal sources.

Both frameworks consistently identified human-to-human transmission as a significant contributor to ESC-EC transmission, acting as primary (in the compartmental) and ranked second and third (in the source attribution models) transmission routes. While these findings confirm the importance of human transmission, their significance in the source attribution model was not as pronounced as in prior studies [9,10,60]. While travelers have been found to have a limited impact, they carry a risk of introducing new ESC-EC strains into Denmark, highlighting the importance of monitoring international travel and its contribution to antimicrobial resistance (AMR) epidemiology [61].

The compartmental model estimated a total of 61,067 E. coli cases in the final year of simulation. In 2023, E. coli isolates exhibited the highest resistance to ampicillin (34–41%), a beta-lactam antibiotic, with 55,762 human isolates reported [14]. This number is slightly lower than both the 2022 data (58,445 isolates [16]) and the model’s projections. However, as resistance to multiple beta-lactams, including those linked to ESBL production, contributes to a broader resistance profile, the estimated case numbers may better align with surveillance data when accounting for additional ESBL-associated antibiotics.

Transmission from food also plays a key role in ESC-EC transmission, with imported food emerging as more impactful. The compartmental model highlights imported pig products as a major source, whereas the source attribution models identify imported turkey as highly important. By contrast, domestic sources such as broilers, cattle, and pigs had a relatively lower impact in the source attribution models. As the source attribution models are attributing to the reservoir level, these models do not distinguish between livestock and food, as the underlying assumption is that the subtypes distributions in animals and the corresponding food types are very similar. However, the compartmental framework revealed a pronounced impact of livestock when considering direct transmission to farmers, with pigs ranking among the top five sources. Earlier studies indicated that direct contact between farmers and livestock increases the likelihood of transmitting ESBL genes [5,9,62]. While the compartmental model captures the effect of increased contact, the source attribution models do not reflect this. In addition, the human isolates used in the source attribution models are probably not from farmers but rather from the general population or pet owners. Since farmers constitute only a small fraction of the total population, their contact with livestock is less clear in the attribution models.

Pets contributed less to overall transmission, yet dogs emerged as the most significant pet-related source, accounting for 20.3% of cases in the “infected” model. Although their role is limited, the findings suggest that pets could be a target for specific interventions to mitigate transmission further. The assumption of farmers not being pet owners is considered to have only a very small impact on the accuracy of the overall result of the contribution from pets, since farmers only constitute a small proportion of the population and even fewer of them would own pets.

The compartmental model estimated that infected individuals who received antibiotics accounted for 3.2%. Although this percentage may seem small, it highlights the potential impact of interventions, such as vaccines, targeting recurrent urinary tract infections [63].

The source attribution models provided insights into the resistance genes contributing to ESC-EC transmission. Common genes such as CMY-2, CTX-M-1, CTX-M-14, CTX-M-15, CTX-M-55, and SHV-12 were detected across multiple sources, while others like CMY-4 were limited to a few specific sources. This highlights the complexity of resistance patterns and the need for comprehensive genomic surveillance.

One limitation of our study is the focus on ESBL-resistant infections, excluding sensitive strains, which limits the broader applicability of our findings. Expanding future analyses to include all E. coli infections could provide a more comprehensive understanding of transmission dynamics and the potential impact of interventions, such as vaccination.

Differences in data origins and temporal trends could have constrained the accuracy of the source attribution models. For instance, data on infected individuals were collected in Denmark from 2018 onward, while open community isolates originated from Sweden and Norway and were sampled in 2012–2013 and 2015–2016 [23,24]. The Norwegian study found that strains from the open community often differed and had lower pathogenicity than bloodstream infections. This highlights the importance of accounting for temporal trends to better capture changes in resistance patterns when modeling.

Integrating more discriminative data on sequence types or phylogenetic groups could improve the precision of these models, potentially making non-human sources less impactful in studies [60]. However, this would reduce the total number of isolates available. Additionally, the limited sampling of specific sources raises questions about whether the observed patterns reflect actual biological constraints or incomplete data. Applying a Dirichlet distribution helped account for uncertainty in gene prevalence estimates, but more extensive sampling is needed to enhance model robustness [58].

This study takes two different approaches to link transmission between animals and humans. The compartmental model’s “bottom–up” approach, tracing transmission from animals to humans, and the source attribution models’ “top–down” approach, linking humans back to animal sources, provided complementary perspectives. However, both frameworks are unidirectional, overlooking interactions such as farmer-to-livestock or pet owner-to-pet transmission [7].

Incorporating multi-directional transmission dynamics could provide more comprehensive insights, as demonstrated by one study on chicken farmers [11].

Although our models accounted for cross-border food trade by distinguishing between domestic and imported meat sources, they did not address environmental (e.g., crops) and wildlife transmission pathways, which are critical components of the One Health framework [64]. Including these reservoirs in future models could provide a more comprehensive perspective on ESC-EC transmission.

Our findings support prioritizing interventions to reduce ESC-EC prevalence in specific sources, such as imported food products and livestock. The compartmental model can serve as a baseline to estimate the impact of interventions, including targeted vaccination programs for high-risk groups, such as farmers, or efforts to reduce resistance in key food sources. These strategies could enhance public health outcomes and inform policies to combat AMR within the One Health paradigm.

5. Conclusions

This study demonstrates the utility of integrating diverse modeling frameworks to unravel the complex transmission dynamics of ESC-EC. While highlighting the dominant role of human transmission, it identifies key sources for targeted interventions. It underscores the importance of robust and representative data collection, comprehensive genomic surveillance, and integrative modeling approaches to address AMR effectively.