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Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39232037
70741
10.1038/s41598-024-70741-8
Article
Quantifying trade-offs between therapeutic efficacy and resistance dissemination for enrofloxacin dose regimens in cattle
Chandra Deb Liton lchandr@ncsu.edu

1
Timsina Archana 1
Lenhart Suzanne 2
Foster Derek 1
Lanzas Cristina 1
1 grid.40803.3f 0000 0001 2173 6074 Department of Population Health and Pathobiology, College of Veterinary Medicine, North Carolina State University, Raleigh, NC 27695 USA
2 https://ror.org/020f3ap87 grid.411461.7 0000 0001 2315 1184 Department of Mathematics, University of Tennessee, Knoxville, TN USA
4 9 2024
4 9 2024
2024
14 2059826 3 2024
20 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
The use of antimicrobial drugs in food-producing animals contributes to the selection pressure on pathogenic and commensal bacteria to become resistant. This study aims to evaluate the existence of trade-offs between treatment effectiveness, cost, and the dynamics of resistance in gut commensal bacteria. We developed a within-host ordinary differential equation model to track the dynamics of antimicrobial drug concentrations and bacterial populations in the site of infection (lung) and the gut. The model was parameterized to represent enrofloxacin treatment for bovine respiratory disease (BRD) caused by Pastereulla multocida in cattle. Three approved enrofloxacin dosing regimens were compared for their effects on resistance on P. multocida and commensal E. coli: 12.5 mg/kg and 7.5 mg/kg as a single dose, and 5 mg/kg as three doses. Additionally, we explored non-FDA-approved regimes. Our results indicated that both 12.5 mg/kg and 7.5 mg/kg as a single dose scenario increased the most the treatment costs and prevalence of P. multocida resistance in the lungs, while 5 mg/kg as three doses increased resistance in commensal E. coli bacteria in the gut the most out of the approved scenarios. A proposed non-FDA-approved scenario (7.5 mg/kg, two doses 24 h apart) showed low economic costs, minimal P. multocida, and moderate effects on resistant E. coli. Overall, the scenarios that decrease P. multocida, including resistant P. multocida did not coincide with those that decrease resistant E. coli the most, suggesting a trade-off between both outcomes. The sensitivity analysis suggests that bacterial populations were the most sensitive to drug conversion factors into plasma (β), elimination of the drug from the colon (ϑ), fifty percent sensitive bacteria (P. multocida) killing effect (Ls50), fifty percent of bacteria (E. coli) above ECOFF killing effect (Cr50), and net drug transfer rate in the lung (γ) parameters.

Keywords

Enrofloxacin dosing regimens in cattle
Antimicrobial drug resistance
PK-PD model
Subject terms

Epidemiology
Computational models
US National Institutes of HealthR35GM134934 issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Antimicrobial drugs are used in food-producing animals to treat, control, and prevent infections. In the United States, the Food and Drug Administration (FDA) approves antimicrobial drugs intended for food-producing animals1. In addition to ensuring the safety and effectiveness of the drug in the target species, the FDA evaluates the drugs based on whether there is reasonable certainty that their use in food-producing animals will not harm human health1. For antimicrobial drugs, a specific consideration is whether the drug can cause resistance and how resistance to the drug can impact public health1. Recently, the FDA proposed a risk assessment approach to evaluate the potential microbial food safety risks associated with new antimicrobial drugs2. While the proposed risk assessment is qualitative, the FDA encourages the use of modeling approaches that can refine and improve the approach and assumptions incorporated in this risk assessment process2.

Ideally, antimicrobial drug use should be optimized to achieve therapeutic efficacy while minimizing the emergence of antimicrobial drug resistance in both pathogens and host-associated commensal bacteria. Dissemination of resistance in the gut bacteria is of particular concern as the gut of food animals is a reservoir for foodborne pathogens3. Emergence and further dissemination of resistance depends on multiple factors, including the antimicrobial drug concentrations to which bacteria are exposed, the genetic basis of resistance, and the relative fitness of the resistant organisms4. These factors can be explicitly addressed and evaluated in mathematical models. Mathematical models grounded on pharmacokinetics (PK), pharmacodynamics (PD), and microbial growth dynamics can provide a risk assessment of the effects of dose and treatment duration on bacterial dynamics5. Overall, only a few mathematical models address the emergence and dissemination of antimicrobial resistance during treatment in food animals6–8. It is unknown what the effect of currently approved dose regimes is on the emergence of resistance in off-target bacteria such as commensal gut bacteria.

Bovine respiratory disease (BRD) is one of the most common diseases affecting feedlot cattle, causing high mortality, reduced performance, and decreased carcass value9,10. BRD is also one of the most common indications for giving individual-level treatment to feedlot cattle9,10. Enrofloxacin—a veterinary-approved fluoroquinolone—is a common choice for BRD treatment because of its high potency against the gram-negative aerobic bacteria that commonly cause BRD, such as Mannheimia haemolytica and Pasteurella multocida11,12. However, there are concerns that the use of enrofloxacin has contributed to the emergence of fluoroquinolone resistance in some foodborne pathogens, such as Campylobacter spp. in calves13,14.

The main goal of this project is to study whether there are trade-offs between the treatment efficacy, economic costs, and the level of resistance of pathogenic and enteric commensal bacteria when treating BRD in cattle. We developed and implemented a deterministic mathematical model of within-host P. multocida infection and enteric E. coli. We simulated different treatment regimens (duration and dosage) of enrofloxacin and evaluated their effects on P. multocida infection and resistance, as well as its implications for selecting resistance in off-target bacteria in the gut. Additionally, we performed a sensitivity analysis to identify the PK and PD parameters that influence the most resistance in both the target and off-target bacterial populations.

Materials and methods

Model description

A system of ordinary differential equations was developed to track the dynamics of the antimicrobial drug concentrations and the bacterial populations in the lungs and gut. The model flowchart is presented in (Fig. 1).Fig. 1 Schematic representation of the mathematical model depicting enrofloxacin concentrations in a steer's gastrointestinal and respiratory tracts, and its effects on both E. coli and P. multocida bacteria populations. The compartments S, P, L, and C represent antimicrobial drug concentrations in subcutaneous tissue, plasma, lung, and colon, respectively. Se, Re, Sm, and Rm represent the susceptible and resistant subpopulation of E. coli and P. multocida. Parameters are described in the text.

Enrofloxacin is administered to the subcutaneous compartment S with a dose denoted as S0, given i times at regular intervals T. This input process is mathematically represented by the Dirac function δ(t-iT). The drug is eliminated from the subcutaneous compartment S at a rate of k. The antimicrobial drug enters the plasma at a rate of β k. Within the plasma, the total concentration of both bound and unbound antimicrobial drug is denoted as P. The drug is then transferred from the plasma to the colon and lungs at a net transfer rate of α and γ, respectively. Finally, the drug levels in the colon C and the lungs L are eliminated at rates of ϑ and δ, respectively. All the mentioned rates apply to both enrofloxacin and its metabolized form, ciprofloxacin, combined.

The bacterial populations, E. coli and P. multocida, grow logistically with net growth rates of σ and λ, respectively. The maximum carrying capacity for the E. coli and P. multocida are denoted as Nemax and Nmmax. The net growth rate of a bacterial strain is considered to represent the bacterial fitness at the within host level15. We modeled the fitness costs associated with resistance by including a fractional reduction in the net growth rates, represented by c and p for the resistant E. coli (Re) and resistant P. multocida (Rm) subpopulations, respectively.

The pharmacodynamic effects of enrofloxacin are modeled by a sigmoidal function representing the saturation of the death rate as a function of the antimicrobial drug concentration5. We assume that the concentration required to produce half of the maximum death effect is greater for resistant bacteria than sensitive bacteria, hence Cr50 > Cs50 and Lr50 > Ls50.

The model described above is represented by the system of differential equations given below:dSdt=∑i=0nS0δ0t-iT-KS

dPdt=βKS-α+γP

dCdt=αP-ϑC

dLdt=γP-δL

1 dSedt=σ1-Se+ReNemaxSe-dCC+Cs50Se

dRedt=1-cσ1-Se+ReNemaxRe-dCC+Cr50Re

dSmdt=λ1-Sm+RmNmmaxRm-ηLL+Ls50Sm-ϕSm

dRmdt=1-pλ1-Sm+RmNmmaxRm-ηLL+Lr50Rm-ϕRm

with initial conditions S (0) = 0 mg/kg, P (0) = 0 mg/kg, C (0) = 0 μ/ml, L (0) = 0 μ/ml, Se = 400,000 colony forming units (CFUs), Re = 1000 CFUs, Sm = 40,000 CFUs, Rm = 1000 CFUs.

Data and model parameterization

The experimental data used to partially parameterize the model were previously described in Foster et al.16,17 and was approved by the North Carolina State University Institutional Animal Care and Use Committee. Moreover, Foster et al.16,17 affirmed adherence to animal welfare and ARRIVE guidelines in their study, demonstrating meticulous attention to ethical standards and methodological rigor. The data for fitting the PK components of the model were collected from two experimental studies where a cohort of twelve steers were monitored following two approved dosing scenarios: a single dose of enrofloxacin (12.5 mg/kg), and a single dose of enrofloxacin (7.5 mg/kg), both administered subcutaneously. After the subcutaneous administration, enrofloxacin concentration in plasma, colon, and interstitial fluid were measured over time. Additionally, E. coli concentration in the gut, measured as CFU/ml, and its minimum inhibitory concentration (MIC) was determined according to the established guidelines of the Clinical and Laboratory Standards Institute6. To capture the changes of overall bacteria population in the model, we denoted the sub-population of E. coli and P. multocida with MICs above the epidemiological cut-off (ECOFF) value as resistant (Re and Rm), and those below the cut-off point were defined as susceptible (Se and Sm). The ECOFF value for enrofloxacin on E. coli and P. multocida is the same, 0.125 μg/ml18,19.

Parameters that can be derived uniquely from the data are considered identifiable20,21. Structural identifiability is a theoretical way to determine whether the within-host ODE model’s parameters are identifiable from the noise-free observations without the actual data22. A structurally unidentifiable parameter obtained from fitting is not valid for further analysis of the ODE model20,21,23. In our model, we investigated the structural identifiability of the parameters before estimating their values. We used a user friendly and universally accessible web application COMBOS24 for checking structural identifiability. COMBOS uses a Grobner-based computation to check the structural identifiability of the parameters24.

We used the software Monolix 2020 R1 (Lixoft, Antony, France) to estimate the PK parameters from the data. We independently fitted the model to the concentration of antimicrobial drugs in the plasma, colon, and lung, and susceptible and resistant E. coli population in the feces for each steer in the treatment groups. The parameter estimation was done using stochastic approximation expectation maximization (SAEM). SAEM is a technique that combines maximum likelihood estimation with stochastic approximation to estimate conditional expectations25. We performed a maximum of 200 Monte Carlo runs, each with 10,000 iterations. The parameters k, Cs50, Ls50, Lr50 were fixed based on previous studies, as shown in Table 1. In our PK-PD model, we assumed all the parameters had log-normal distributions. Also, we let σ, d, and Nemax vary across study populations to capture the dynamics of E. coli at the individual level. The reason to estimate those parameters is that commensal E. coli populations typically vary across individuals and can be highly dynamic26. Using the data from Foster et al.17, we estimated β, α, ϑ, σ, and Nemax. Also, by using data from Foster et al.16, we estimated γ, d and δ. Then Nmmax, λ, c, η, p, and ϕ values were calibrated to a scenario in which the disease-causing P. multocida bacteria was cleared in the model.Table 1 Parameter values from literature, calibration, and estimation. Here, aindicates that parameters value used to clear the infection scenario.

Parameters	Description	Values	Units	Source	
k	Drug absorption rate into plasma	0.44	h-1	Erwin et al. 20206	
β	Drug conversion factor into plasma	0.0016	μgmg-1kgmL-1	Estimated	
α	Net drug transfer rate in colon	0.16	h-1	Estimated	
ϑ	Elimination of drug from colon	0.53	h-1	Estimated	
σ	E. coli growth rate	0.28	h-1	Estimated	
Nemax	Maximum bacteria (E. coli) concentration	484,577	CFUsg-1	Estimated	
Cs50	Fifty percent of sensitive bacteria (E. coli) killing effect	0.25	μgmL-1	Liu et al., 202127	
Cr50	Fifty percent of bacteria (E. coli) above ECOFF bacteria killing effect	0.471	μgmL-1	Calibrated	
d	Death rate of E. coli	1.01	h-1	Calibrated	
c	Fitness cost of E. coli	0.05		Calibrated	
γ	Net drug transfer rate in lung	0.16	h-1	Estimated	
λ	P. multocida growth rate	0.25	h-1	Calibrated	
Nmmax	Maximum bacteria (P. multocida) concentration	512,861	CFUsg-1	Calibrated	
Ls50	Fifty percent of sensitive bacteria (P. multocida) killing effect	0.016	μgmL-1	Bello et al., 201919	
Lr50	Fifty percent of bacteria (P. multocida) above ECOFF bacteria killing effect	0.125	μgmL-1	Bello et al., 201919	
δ	Elimination of drug from lung	0.24	h-1	Estimated	
η	Death rate of P. multocida	0.40	h-1	Calibrated	
p	Fitness cost of P. multocida	0.05, 0.10a		Calibrated	
ϕ	Immunological death rate	0.14, 0.22a	h-1	Calibrated	

The model was run in R software version 4.3.1. The integrator used in our model is lsoda from the deSolve package (version 1.40) in R software version 4.3.1. lsoda is a robust numerical solver that automatically switches between non-stiff and stiff integration methods.

Simulated scenarios

In our study, we simulated the impact of three approved enrofloxacin dosing scenarios and some non-approved proposed scenarios on the treatment efficacy against one of the causative agents of BRD, P. multocida. Specifically, in the case of approved scenarios, we simulated 12.5 mg/kg and 7.5 mg/kg as a single dose, and doses of 5 mg/kg given 24 h apart for three days, all administered subcutaneously. In case of proposed non-approved dosing scenarios, we simulated doses of 12.5 mg/kg, 7.5 mg/kg, 6.25 mg/kg, and 3.75 mg/kg, administered 24 h apart for 2 days. Additionally, we examined doses of 4.15 mg/kg, given subcutaneously 24 h apart for three consecutive days. Our investigation aimed to simulate the effects of these drug dosing regimens and gain insights into their therapeutic efficacy, treatment cost, and bacterial resistance outcomes.

Our study assessed the treatment expenses associated with different dosing scenarios. To quantify each treatment scenario’s cost, we considered the average cost of medications and labor and the productivity losses resulting from the treatment process28. If the infection was not fully resolved (defined in the model as presence of bacteria in the lung after treatment), we added an additional treatment in our analysis.

Uncertainty and sensitivity analysis

To identify the PK and PD parameters that have the most influence on the bacterial resistance within the lung and gut sites, Rm and Re, we performed a variance-based sensitivity analysis. This Sobol sensitivity approach uses model output uncertainty to describe the variance29,30. We have chosen to vary the following PK and PD parameter set, q = (k, β, α, γ, ϑ, δ, Cs50, Cr50, Ls50, Lr50). As a model output, we evaluated the uncertainty of both the susceptible and resistant of E. coli and P. multocida bacterial populations. We calculated the first-order and total-order Sobol indices of the parameter set q for the resistant bacteria31–33. The basic algorithm for the calculation of the indices is as follows:Providing lower and upper bound values for each parameter of q as an input, we obtain N possible values uniformly distributed for each of the parameters of q.

Taking the distributions of the set of parameters q as an input variable, the within-host model (1) generates N = 2000 set of solutions, also called uncertainty distribution of solutions. In this study, we focus on the uncertainty distribution of states Se(t), Re(t), Sm(t), and Rm(t).

As mentioned, we are only concerned with calculating the Sobol indices of Rm and Re. Here, we calculated the overall variance of the resistant using deviation from the average value of the time-dependent uniform distribution of the resistant. Let the overall variance of Rm be denoted by VRm.

The first-order variance VSi of Rm is calculated with respect to an individual parameter qi of the set q.

The total-order variance VTi of Rm is calculated with respect to all parameters except the individual parameter qi of the set q.

The time-dependent first-order Sobol index of the parameter qi for Rm is calculated with the formula Si = VSiVRm and the time-dependent total-order Sobol index of the parameter qi for Rm is calculated with the formula Ti = 1 − VTiVRm.

The sum of the first-order indices of all parameters q such as ∑iSi is less than 1. Similarly, ∑iTi also is less than 1. If Si or Ti of a parameter is close to 1, then that parameter significantly influences the state Rm. On the other hand, if Si or Ti of a parameter is close to 0, that parameter has low influence on the state Rm.

As the indices Si(t) and Ti(t) of each parameter of set q are time dependent, we plotted the curves of the indices over time T = 150 h

The curve thus created by the indices of each parameter of q over time 150 h is integrated to get area using the Riemann sum. These areas help us to compare the level of sensitivity of parameters of set q for Rm for the complete simulation period.

Similarly, we repeated the similar process of finding Sobol indices and integrated area for Re.

We used the “Sensobal package” (version 1.1.5) of R software version 4.3.1 to calculate the Sobol indices33,34.

The input bounds for q, the generated uniform distribution of states Se, Re, Sm, and Rm as well as the results of Sobol indices of the model parameters q for resistant bacteria Rm and Re are presented in the results section. We utilized the proposed value for each parameter in Table 1 and select upper and lower bounds not more than 3 standard deviations from each parameter of set q. Each parameter’s upper and lower bounds of q are in Table 2Table 2 The lower and upper bound of the set of parameters q, which are applied to perform the Sobol sensitivity analysis in the ‘Sensobal package’ (version 1.1.5) of R software version 4.3.1. We iterated the simulation 2000 times and used a uniform distribution of each parameter of set q.

Parameters (q)	Lower bound	Upper bound	
k	0.04	0.9	
\beta	0.0001	0.005	
α	0.01	0.5	
γ	0.01	0.5	
ϑ	0.05	0.9	
δ	0.07	0.7	
Cs50	0.2	0.45	
Cr50	0.3	0.9	
Ls50	0.006	0.06	
Lr50	0.05	0.13	

Results

Simulated case scenarios

We chose specific parameters values to reflect two types of case scenarios; one in which the approved doses clear the P. multocida infection (Fig. 2), and one in which the infection was not cleared for all the approved doses (Fig. 3). For both types of scenarios, the multiple-dose regimen (5 mg/kg, three times) was predicted to clear P. multocida infection. While at the assumed resistance level for P. multocida, the two single dose regimens failed to clear the infection, and P. multocida numbers rebounded after treatment ended (Fig. 3c,d). On the contrary, the multiple-dose regimen had a greater effect on the commensal E. coli bacteria resistance levels in the gut when compared to the two single dose scenarios (Fig. 3b), indicating the differential antibiotic effect on the different body sites and bacteria populations.Fig. 2 Dynamics of bacterial (E. coli) and (P. multocida) population under approved dosing scenarios where infection is cleared: (a) Susceptible E. coli (Se), (b) Resistant E. coli (Re), (c) Susceptible P. multocida (Sm), (d) Resistant P. multocida (Rm). In this case parameters P = 0.10 and ϕ = 0.22 were used.

Fig. 3 Dynamics of bacterial (E. coli) and (P. multocida) population under approved dosing scenarios: (a) Susceptible E. coli (Se), (b) Resistant E. coli (Re), (c) Susceptible P. multocida (Sm), (d) Resistant P. multocida (Rm).

While the two single dose scenarios showed a reduced level of commensal E. coli bacteria resistance in the gut (Fig. 3b), they fell short of effectively curing the infection (Fig. 3c,d). Moreover, these two single doses of enrofloxacin administration seemed to correlate with an increase in the prevalence of resistance P. multocida bacteria in the lungs (Fig. 3d).

Our study explored some proposed non-FDA-approved dosing scenarios by modifying the quantity and frequency of drug administration to the cattle. The goal was to investigate whether dose regimens had similar effects in both the pathogen and the off-site bacteria. Trends like the ones in the approved regimes scenarios were observed. The greater the dose and frequency, the larger the resistant E. coli population after the treatment (Fig. 4.) Among the tested dose regimens, 3.75 mg/kg administered twice had the greater increase of drug-resistant P. multocida bacteria (Fig. 4d). In contrast, a reduced number of resistant commensal E. coli bacteria was noted in the gut (Fig. 4b).Fig. 4 Dynamics of bacterial (E. coli) and (P. multocida) population under non-approved proposed dosing scenarios: (a) Susceptible E. coli (Se), (b) Resistant E. coli (Re), (c) Susceptible P. multocida (Sm), (d) Resistant P. multocida (Rm).

When comparing the cost associated with different doses, the 7.5 mg/kg given twice with a 24-h interval was the most cost-effective (Table 3). This treatment cleared the infection within 48 h and had a moderate effect on the resistant E. coli population in the gut (Fig. 4b,d).Table 3 Cost and infection outcomes associated with different treatment scenarios. Here, aindicates that infection was not clear, and bacteria were still present.

Dosing scenario	Time required to cure infection (h)	Accumulative resistant E. coli (%)	Treatment cost ($)	Additional treatment if uncured ($)	Total cost ($)	
12.5 mg/kg-twice	45	34.65	64	0	64	
12.5 mg/kg-once	N/Aa	1.84	43	43	86	
7.5 mg/kg-twice	48	22	41	0	41	
7.5 mg/kg-once	N/Aa	1.37	37	37	74	
6.25 mg/kg-twice	52	18.35	48	0	48	
5 mg/kg-three	53	15.01	46	0	46	
4.15 mg/kg-three	47	67.56	69	0	69	
3.75 mg/kg-twice	N/Aa	9.45	42	42	84	

Uncertainty and sensitivity analysis results

Following the algorithm mentioned in the methods section, we simulated the model outcomes for the three approved scenarios for 2000 simulations across the uniform distribution for the PK and PD parameters on Table 2. Figures 5, and 6 show the uncertainty of each susceptible and resistant bacteria of E. coli and P. multocida correspondingly in the case of single dose scenario 12 mg/kg and multiple doses scenario 5 mg/kg. As the uncertainty of single dose scenario 7.5 mg/kg shows a distribution identical to that of single dose scenario 12 mg/kg, we presented the 7.5 mg/kg plot in a Supplementary Fig. 1. We observed the uncertainty of resistant and susceptible P. multocida bacteria with the multiple doses scenario 5 mg/kg is had a narrow spread; otherwise, the uncertainty of both bacteria in all other scenarios is had a widespread. These were uniformly distributed parameters as outlined in Table 2. Most importantly, we noted that the median value for resistant and susceptible bacteria of E. coli and P. multocida matches the dynamic of approved cases presented in Fig. 3. This implies that the lower and upper bounds of the parameters of Table 2 for uniform distribution are one of the optimal sets for the variance-based Sobol sensitivity analysis of the parameters.Fig. 5 Uncertainty of the states: (a) susceptible of E. coli (Se), (b) susceptible of P. multocida (Sm), (c) resistant of E. coli (Re), and (d) resistant of P. multocida (Rm). These distributions for the ODE solutions of model (1) when the parameter set is varied according to the uniform distributions given in Table 2. In this case, the treatment is 12.5 mg/kg single dose. The dark red curves represent the average solution curves (median) of the states obtained from the uncertainty distribution. Other light pink, pink, and dark pink ribbons represent the solutions in 25–75 quantiles of the uncertainty distribution of states.

Fig. 6 Uncertainty of the states: (a) susceptible of E. coli (Se), (b) susceptible of P. multocida (Sm), (c) resistant of E. coli (Re), and (d) resistant of P. multocida (Rm). These distributions are by ODE solution of model (1) for 150 h having the uniformly distributed parameters input given in Table 2. In this case, the drug dose is 5 mg/kg three times. The dark red curves represent the average solution curves (median) of the states obtained from the uncertainty distribution. Other light pink, pink, and dark pink ribbons represent the solutions in 25–75 quantiles of the uncertainty distribution of states.

Herein, we calculated the sensitivity indices of the PK and PD parameters on Table 2 for the bacterial resistant Rm and Re in the model (1) with all the three approved doses cases scenario (see Figs. 7, 8,9,10,11, and 12). First-order and total-order Sobol indices changed with time, making it difficult to decide which parameter the resistant bacteria population is more sensitive to. We then calculated the integrated area of each curve over 150 h using the Riemann sum method to compare the parameters’ sensitivity levels to the parameters. Tables 4, 5, and 6 present the integrated area for all three cases. The results revealed that changes in the parameter β, ϑ, and Cr50 significantly affect the model outputs for Re and Rm in the case of single dose scenario of 12 mg/kg (Table 4). Similarly, for the single dose scenario 7.5 mg/kg, the parameters β, ϑ, and Ls50 are the most influential parameters on the model outputs for the resistant bacteria Re and Rm (Table 5). Whereas, in the case of multiple doses scenario of 5 mg/kg, changes in the parameters β, γ, and Cr50 are most sensitive on the model outputs for Re and Rm (Table 6).Fig. 7 Time-dependent Sobol indices of the set parameters q for the resistance of P. multocida (Rm) over a time period of 150 h. In this case, the treatment is 12.5 mg/kg single dose. Some parameters are from the uniform distribution given in Table 2, and others are from Table 1. The (a) shows first-order Sobol indices for P. multocida (Rm). Likewise, the (b) shows the total-order Sobol indices for P. multocida (Rm).

Fig. 8 Time-dependent Sobol indices of the set parameters q for the resistance of E. coli (Re) over a time period of 150 h. In this case, the treatment is 12.5 mg/kg single dose. Some parameters are from the uniform distribution given in Table 2, and others are from Table 1. (a) Shows the first-order Sobol indices E. coli (Re). Likewise, the (b) shows the total-order Sobol indices for E. coli (Re).

Fig. 9 Time-dependent Sobol indices of the set parameters q for the resistance of P. multocida (Rm) over time period 150 h. In this case, the drug dose is 7.5 mg/kg single time. Some parameters are from the uniform distribution given in Table 2, and others are from Table 1. The (a) shows the first-order Sobol indices for P. multocida (Rm). Likewise, the (b) shows the total-order Sobol indices for P. multocida (Rm).

Fig. 10 Time-dependent Sobol indices of the set parameters q for the resistance of E. coli (Re) over time period 150 h. In this case, the drug dose is 7.5 mg/kg single time. Some parameters are from the uniform distribution given in Table 2, and others are from Table 1. The (a) is the first-order Sobol indices for E. coli (Re). Likewise, the (b) is the total order Sobol indices for E. coli (Re).

Fig. 11 Time-dependent Sobol indices of the set parameters q for the resistance of P. multocida (Rm) over time period 150 h. The drug dose is 5 mg/kg three times in this case. Some parameters are from the uniform distribution given in Table 2, and others are from Table 1. The (a) is first-order Sobol indices for the P. multocida (Rm). Likewise, the (b) is the total- order Sobol indices for P. multocida (Rm).

Fig. 12 Time-dependent Sobol indices of the set parameters q for the resistance of E. coli (Re) over a time period of 150 h. The drug dose is 5 mg/kg three times in this case. Some parameters are from the uniform distribution given in Table 2, and others are from Table 1. The (a) is the first-order Sobol indices for E. coli (Re). Likewise, (b) is the total-order Sobol indices for E. coli (Re).

Table 4 Area obtained by integrating the Sobol indices curves over 150 h when drug dose is 12.5 mg/kg single time.

Integrated area under the indices curve	
Parameters	First-order	Total-order	
Rm	Re	Rm	Re	
k	11.81	9.67	15.96	24.96	
β	26.65	14.87	83.06	49.17	
α	7.49	7.78	22.15	26.89	
γ	18.24	4.96	44.72	26.17	
ϑ	4.96	12.92	1.49×10-10	54.34	
δ	8.36	5.57	38.23	1.59×10-9	
Cs50	4.96	17.66	2.08×10-10	38.67	
Cr50	4.96	23.22	3.87×10-11	53.06	
Ls50	8.78	5.57	46.12	8.16×10-9	
Lr50	8.31	5.57	18.02	4.79×10-10	

Table 5 Area obtained by integrating the Sobol indices curve over time 150 h when drug dose is 7.5 mg/kg single time.

Integrated area under the indices curve	
Parameters	First-order	Total-order	
Rm	Re	Rm	Re	
k	10.40	5.23	18.82	17.42	
β	35.92	10.88	89.66	44.03	
α	15.89	4.89	24.97	21.30	
γ	20.16	2.82	45.38	22.89	
ϑ	1.56	17.98	2.51×10-10	64.93	
δ	19.46	1.61	42.93	6.29×10-10	
Cs50	1.56	23.18	3.2×10-10	42.14	
Cr50	1.56	20.34	8.65×10-11	48.07	
Ls50	22.05	1.61	60.80	6.78×10-10	
Lr50	21.32	1.61	20.91	2.27×10-10	

Table 6 Area obtained by integrating the Sobol indices curve over time 150 h when drug dose is 5 mg/kg three times.

Integrated area under the indices curve	
Parameters	First-order	Total-order	
Rm	Re	Rm	Re	
k	4.51	2.67	2.38	5.41	
β	33.46	8.84	76.77	55.49	
α	7.92	5.30	20.99	27.26	
γ	14.45	2.13	65.31	23.31	
ϑ	3.37	7.53	1.10×10-10	57.81	
δ	5.66	1.54	32.86	5.42×10-10	
Cs50	3.37	14.57	1.08×10-10	39.78	
Cr50	3.37	32.66	7.18×10-11	61.61	
Ls50	9.05	1.54	44.52	4.36×10-10	
Lr50	4.12	1.54	13.72	4.76×10-10	

Discussion

Antimicrobial use in food animals contributes to the emergence of antimicrobial resistance in commensal gut bacteria and foodborne pathogens that can be transferred to humans through the food chain by direct contact or environmental pathways35. The increasing trend of bacterial resistance among food animals has emerged as a growing public health concern36. Additionally, resistance in animal pathogens can lead to treatment failures, increased treatment costs, and reduced sale value37. Limiting antimicrobial use to the shortest effective duration is crucial for maintaining maximum efficacy while reducing the dissemination of AMR38. It is unclear if current dose regimens can both minimize resistance at the site of infection and on off-target bacteria, such as commensal gut bacteria. The interplay between the dosing magnitude, dosing frequency, and bacterial resistance dynamics in both the side of infection and the gut is unknown. Mathematical models can help to elucidate the underlying relationships between the extent of antimicrobial usage and the dynamics of bacterial populations in the gut microbiota7,39,40. In this paper, we combined a mathematical model of drug and bacteria dynamics with parameter inference using PK-PD modeling tools. This approach enabled us to characterize the uncertainty and its effects on model outcomes.

Our model captures the changes in the bacterial dynamics caused by the competitive release of resistant strains and further selection mediated by enrofloxacin treatment. The dose at which these events have a greater effect in the commensal E. coli and P. multocida varies. For example, among the approved dosing scenarios, 5 mg/kg as three doses increased the resistance levels in commensal gut enteric E. coli bacteria the most. However, the same dose effectively cleared the P. multocida infection and minimized its resistance. These findings align with prior literature, which has noted that antimicrobial treatment rapidly increases the pool of resistance genes within the gut41. Conversely, our investigation revealed that the approved two single dose scenarios to treat BRD infection increased the prevalence of resistant pathogenic P. multocida bacteria in the lungs in our simulations. This increased prevalence is the result of higher bacterial fitness42.

The sensitivity analysis indicated that the model outcomes were particularly sensitive to parameters drug conversion factors into plasma (β), elimination of the drug from the colon (ϑ), fifty percent sensitive bacteria (P. multocida) killing effect (Ls50), fifty percent of bacteria (E. coli) above ECOFF killing effect (Cr50), and net drug transfer rate in the lung (γ).

Our cost analysis considers the most immediate costs associated with treatment failure (i.e., additional treatment, and productivity losses). Our model findings indicate that the two approved single doses treatment scenarios increased overall treatment costs, primarily due to the need to add a treatment round when the infection persists. On the other hand, multiple doses cleared the infection, but they were associated with a cost of a higher number of resistant commensal E. coli. The proposed non-FDA-approved 7.5 mg/kg administered twice in a 24-h interval had the lowest cost and overall resistant bacteria. This treatment scenario cleared the infection within a 48-h and offered the advantage of a lower overall treatment cost. Using fluoroquinolones in an unapproved manner is illegal in food animals in the United States, so while this regimen may be the most advantageous in this model, we are not advocating for the illegal, extra-label use of enrofloxacin.

Our study was limited by using data to fit the model from experiments conducted on healthy steers. Further research is needed to fully understand how the drug works in animals with respiratory diseases. Additionally, since our data came from healthy animals, we needed more experimental data related to BRD. To address this, we relied on information from existing literature to supplement our model.

Conclusion

In our model, the dose regimens that minimize infection differ from those that minimize resistance in commensal E. coli bacteria. Our model’s results underscore the significance of optimizing the currently approved treatment dosing scenarios for treating BRD and using effective antimicrobial treatments in the shortest duration to prevent the spread of AMR.

Supplementary Information

Supplementary Figure 1.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-70741-8.

Acknowledgements

This work was supported by the US National Institutes of Health (NIH) (R35GM134934). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funder. The author would also like to thank Manuel Jara for drawing Fig. 1.

Author contributions

L.C.D. led the model creation, data analysis, and manuscript writing. Both L.C.D. and C.L. conceived the ideas presented here and C.L. secured the funding. A.T. carried out the sensitivity analyses. All authors contributed to the model development, writing drafts and gave final approval for publication.

Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on request. Relevant code used in this study can be found at https://github.com/lanzaslab/withinhost.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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