Abstract
Antibiotic resistance is becoming one of the threats to global health. This crisis has been attributed to the overthecounter and overuse of antibiotics leading bacteria to gain the ability to resist and survive even in the presence of antimicrobial agents. Escherichia coli (E. coli) is one of the major gramnegative bacteria that are the representative indicators of antibiotic resistance. One of the mechanisms of gaining antibiotic resistance is the ability of E. coli to gain the production of extendedspectrum betalactamases (ESBL). In this study, Near East University Hospital data from 2016 to 2019 were used to study the dynamics of ESBLproducing (
1 Introduction
Microorganisms in the Enterobacteriaceae family are the most frequently isolated gramnegative bacteria group from clinical specimens. One example is Escherichia coli (E. coli), which is a member of the human intestinal normal flora but can also be the cause of infections like urinary tract infections, hemolytic uremic syndrome, pneumonia, sepsis, meningitis, diarrhea, etc. [1].
In the last decade, bacteria developing resistance to available antibiotics has become a global threat worldwide. One of the biggest reasons for this is the inappropriate and overthecounter use of antibiotics. Resistance development in gramnegative bacteria against betalactam antibiotics is due to the widespread inappropriate use of new betalactam antibiotics. Bacteria acquire resistance by gaining the property of producing the betalactamase enzyme. These enzymes destroy the antibacterial effect by breaking the amide bonds in the betalactam ring of betalactam antibiotics [2,3].
One of the most important resistance mechanisms against betalactam group antibiotics is the production of extendedspectrum betalactamase (ESBL). ESBLproducing Enterobacteriaceae isolates are common human pathogens that pose serious problems for individual and public health [4]. Infections originating from ESBL producing E. coli strains can lead to longterm hospitalization, high treatment costs, and high mortality rates [5,6].
The first choice of antibacterial agent in the treatment of ESBL producing gramnegative bacterial infections is the carbapenem antibiotic group. Similar to betalactam group antibiotic, resistance development in the carbapenem antibiotic group is seen frequently due to the widespread and inappropriate use of carbapenems [7]. Carbapenemresistant Enterobacteriaceae isolates can also be resistant to many other antibiotics and are considered virulent pathogens. Therefore, serious measures must be taken to prevent the spread of these microorganisms [8].
The distribution of microorganisms that cause infectious diseases and their resistance to antibiotics have changed over the years. For this reason, changes in the causative microorganism and antibiotic resistance status should be constantly monitored by each laboratory to guide the application of empirical treatment [9].
Mathematical modeling is often used to analyze the dynamics of infectious diseases such as influenza, childhood infections, HIV, or vectorborne infections. It has been a widely used technique in recent years for the generation of heath policies as well as supporting the control strategies development of infectious diseases [10,11]. Also, simulations applied in a mathematical model are used to forecast ongoing epidemic spread within the studied population [12]. In addition, with the emergence of coronavirus disease 2019 (COVID19) pandemic, many studies have successfully used mathematical modeling to control and develop countrybased health policies [12,13]. The applied mathematical models generally aim to predict the recurrence, spread, and mortality rates of the disease and to explain their causes [14,15].
In this study, culture samples of patients who were admitted to the Near East University (NEU) Hospital between 2016 and 2019 were evaluated. A mathematical model was created with the data determined and obtained retrospectively. The mathematical model used in this study is
The very important threshold quantity of the mathematical model is the basic reproduction number denoted as R _{0} which is an epidemiologic metric used to analyze the dynamics of infectious diseases. The R _{0} is generally reported as a single numeric value and the magnitude of R _{0} value is indicative of a potential size of an outbreak or epidemic within the studied population. Interpretations of the R _{0} value are made as follows: if the value is equal to or above 1 an outbreak is expected to continue. On the other hand, if R _{0} value is below 1, an outbreak is expected to end [17,18].
The created SI type of mathematical model within this study aimed to analyze the antibiotic resistance patterns of E. coli infections and the rate of encountering nonESBL and ESBL producing E. coli infections. This study also aims to reveal the emergence rates of E. coli strains in patients from the cumulative data of patients visiting NEU Hospital from 2016 to 2019.
Before starting this study, research related to mathematical modeling in the literature was examined. It has been seen that mathematical models are used in the analysis of HIV (human immunodeficiency virus) dynamics [11], in different fields for many purposes during the COVID19 pandemic [19], in the followup of parasitic infections like Hookworm infection [20], in modeling the measles epidemic [21], and in studies related to the investigation of immunological tumor dynamics in cancer patients [22]. In addition, this study was aimed because there are almost no modeling studies on bacteria and antibiotic resistance. The absence of any modeling studies on E. coli and antibiotic resistance patterns in Northern Cyprus is one of the main reasons for planning this study.
There are very few articles in the literature about following or predicting the bacteria that cause common diseases and the resistance patterns they develop with mathematical modeling. Our article is especially important in terms of following up E. coli infections taking precautions by monitoring resistance strains, and therefore, reducing mortality and morbidity rates. The main goals of this study were to: (i) emphasize the inappropriate use of antibiotics, which is the main reason for the development of resistance in bacteria, (ii) evaluate the status of ESBL producer E. coli strains in the future, (iii) make assumptions by discussing the increasing problem of antibiotics, and (iv) estimate the ways to combat these problems and to increase the success rates in the treatment of patients infected with E. coli.
The remainder of the article proceeds as follows. In Section 2, collection of E. coli data and applied models are described. In Section 3, the values of the model in numerical simulation and sensitivity analysis of the dynamics of resistant E. coli strains are explained in the light of the data obtained as a result of the modeling. In the last sections, a discussion of the results and concluding remarks are presented.
2 Experimental procedures
2.1 Collection of data
E. coli strains detected in patients who visited the NEU Hospital between 2016 and 2019 were taken from the Nucleus data system in the hospital with their associated predetermined parameters. These parameters included age, gender, and culture samples (urine, blood, aspirate, etc.). Also, the parameters included the departments where these samples arrived from such as internal medicine, intensive care, etc. Furthermore, the strains of E. coli were grouped into ESBL negative and ESBL producing E. coli strains according to their antibiotic resistance profile. In this study, to simplify the flow of the text, ESBL producing E. coli strains are referred to as
2.2 Identification of strains and antimicrobial susceptibility tests
The samples taken from the relevant services and polyclinics of the NEU Hospital during the study period were delivered to the microbiology laboratory. The delivered samples were cultured on blood agar and eosin methylene blue (EMB) agar. These media were kept in an incubator at 35°C for 24–48 h depending on the growth status.
For the samples with gramnegative bacterial growth, McFarland bacterial suspensions in the range of 0.50–0.63 MFU were prepared based on the manufacturer’s recommendations. These prepared suspensions were loaded into the Biomerieux VITEK^{®} 2 Compact (bioMerieux, Inc. Durham, USA) device for identification of the bacterial species and analysis of antimicrobial susceptibility tests. VITEK^{®} 2 GN (bioMerieux, Inc. Durham, USA) cards were used to identify the gramnegative bacterial species. The antimicrobial resistance of the detected bacteria was determined by the type of sample (urine, sputum, etc.) by using VITEK^{®} 2 ASTN327 (bioMerieux, Inc. Durham, USA), VITEK^{®} 2 ASTN325 (bioMerieux, Inc. Durham, USA), and VITEK^{®} 2 ASTN326 (bioMerieux, Inc. Durham, USA) cards.
2.3 Application of obtained data to the mathematical model
The study used SI type of mathematical model. Basic reproduction numbers for E. coli nonESBL and ESBL producing infections were calculated and represented as
In the constructed model, populations within the hospital were grouped into three mutually exclusive ways: The susceptible
Within the created model, the rate of admission to the hospital with infected
Parameters  Descriptions  Values 

S  Susceptible to E. coli  17,579 
E ^{−}  ESBL negative E. coli  1,279 

ESBL positive E. coli  601 

Carbapenems  518 

Piperacillintazobactam  472 

The number of hospital admissions  67.064 

The fraction of patients admitted with

0.5099 

The fraction of patients admitted with

0.0239 

The probability that a person takes drug one and be resistant to the drug  0.7 

The transmission rate of a susceptibility patient infected with

0.00000045 

The transmission rate of susceptible to ESBL^{+} E. coli  0.00000052 

Removed from

0.007819 

Transmission rate from

000655 

Rate of individuals that can be treated with K  0.000861897 
p  Rate of individuals that can be treated with T  0.000078536 

Transmission rate from

0.00218 

Natural death  0.0002 
The most often used treatment options for
It is assumed that the individual with ESBL^{+} can be treated with
2.4 Stability of diseasefree equilibrium (DFE) point and basic reproduction ratio
With equalizing to zero of each equation in the system (2) and with the assumption
By using the nextgeneration matrix method,
Then,
Then, parameters represented in Table 1 were integrated into equations. (3) and (4) and the below values of
Theorem 1
For model (2), the diseasefree equilibrium was locally asymptotically stable when
Proof
The Jacobian matrix at the DFE point of the model (2):□
The eigenvalues of the Jacobian matrix were:
The
Sensitivity analysis of
Local sensitivity analyses were applied in order to highlight the sensitivity of some key associated parameters to the value of
This was performed to analyze the sensitivity of
Then, computation of the normalized local sensitivity was performed which indicates that
By using the
Using the above definition (5), the model was computed by the following indices for the output
3 Results
In this model, the patients who were diagnosed from 2016 to 2019 solely with E. coli strains were used to study E. coli infections and estimate the simulations on the antibiotic resistance analysis. Based on the collected data, sensitivity analysis was applied to each of the parameters indicated in Table 1 within the model. The parameters in Table 1 were integrated into Eqs. (6–17) and the sensitivity analysis for each parameter in
Sensitivity  Sensitivity values 


1 

1 

–0.9599 

–0.98545 

–0.01095 

–1.0036 

1 

1 

–0.87212 

–0.87745 

–0.09817 

–0.01046 
For
Furthermore, dynamics of the E. coli
With the present data, nonESBL E. coli (
3.1 Sensitivity analysis of
R
0
within the model for
E
S
B
L
+
E. coli patients
From here, the rest of the study has emphasized the
The parameter represents the carbapenemase treatment. Figure 3a represents the original data and Figure 3b represents the 10% increase in carbapenemase treatment to the original data. In this way, the model sensitivity could be analyzed. According to our application, when
The parameter
The parameter
The parameter
In the model
In the model,
4 Discussion
This study aimed to investigate the near future possibility of the development of antibiotic resistance to E. coli producing ESBL infections (ESBL^{+}). To carry out this analysis
Moreover, local sensitivity analysis was carried out to evaluate the impact of each parameter used in the model to study the impact on
For this study,
This study was conducted using a total of 17,579 hospital admissions to NEU Hospital in the period between January 2016 and December 2019. Amongst the 17,579 hospital admissions, it was found that 1,871 E. coli infections related to hospital admissions occurred in the study period. According to the analysis of the E. coli infection, 1,270 were found to be
By using the
Furthermore, simulation analysis was performed using the mathematical model and data for NEU hospital for the study period. The dynamics of
From the simulation results, the increasing pattern predicted in the
Another study carried out in 2014 in Cyprus, also emphasized the arising problem of
Furthermore, sensitivity analysis was used to determine which parameters affect the
On the other hand, increasing the death rate
5 Conclusion
In conclusion,
The use of overthecounter antibiotics should be prevented all over the world. Deterrent measures should be strengthened by law to prevent the sale of antibiotics without a prescription. The problems that may be caused by unconscious antibiotic use in the following years should be tried to be shown to people through such studies. In addition, the effective and active functioning of the infection control committee in each hospital and the timely training of all personnel is an important step in slowing down the rate of all infections. This study shows us that when all these are not done, increasing antibiotic resistance will continue to be a major public health problem affecting the whole world.
Selling antibiotics without a prescription may cause bacterial resistance, such as ESBL or carbapenem, in the community. However, it is clear that the spread of resistant bacteria within the hospitals, significantly increases mortality and morbidity rates in patients. For these reasons, effective surveillance studies should be conducted which will provide us with information about these types of infections and give clues for the precautions to be taken in the future. The acceptance and implementation of the concept of “one health” in all countries has an important place among the measures that can be taken. In recent years, the use of mathematical models in health fields gives us the chance to obtain more precise information and to prevent or take early precautions against infections caused by resistant bacteria.

Funding information: The authors state no funding involved.

Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

Conflict of interest: The authors state no conflict of interest.
References
[1] Duman Y, Güçlüer N, Serindağ A, Tekerekoğlu MS. Antimicrobial susceptibility of E. coli strains and presence of extendedspectrum beta lactamase. Fırat Tıp Derg. 2010;15:197–200.Search in Google Scholar
[2] Akova M. Alarm: there are extendedspectrum betalactamases (ESBL)! ANKEM Derg. 2004;18:98–103.Search in Google Scholar
[3] Taşova Y. Management of gramnegative enteric bacteria infections. ANKEM Derg. 2011;25:34–44.Search in Google Scholar
[4] Aydemir Ö, Terzi HA, Şahin Özözen E, Köroğlu M, Altındiş M. Piperacillin/Tazobactam invitro activity in Escherichia coli and Klebsiella pneumonia strains with extended spectrum betalactamase production. OTJHS. 2019;4:118–27. 10.26453/otjhs.487008.Search in Google Scholar
[5] Yılmaz FF, Ermertcan Ş. Investigation of fluoroquinolones resistance in Escherichia coli strains isolated from urinary tract infections. Turkish J Infect. 2005;19:429–33.Search in Google Scholar
[6] Moubareck C, Daoud Z, Hakimé NI, Hamzé M, Mangeney N, Matta, et al. Countrywide spread of community and hospitalacquired extendedspectrum βLactamase (CTXM15)producing Enterobacteriaceae in Lebanon. J Clin Microbiol. 2005;43:3309–13. 10.1128/JCM.43.7.33093313.2005.Search in Google Scholar PubMed PubMed Central
[7] Alpay Y, Yavuz MT, Aslan T, Büyükzengin B. Can oral antibiotics be an alternative to carbapenems in the treatment of noncomplicated urinary tract infections caused by extendedspectrum betalactamase positive Escherichia coli? ANKEM Derg. 2017;31:85–91. 10.5222/ankem.2017.085.Search in Google Scholar
[8] Bayraktar B, Pelit S, Bulut ME, Aktaş E. Trend in antibiotic resistance of extendedspectrum betalactamaseproducing Escherichia coli and Klebsiella pneumoniae bloodstream infections. Med Bull Sisli Etfal Hosp. 2019;53:70–5. 10.14744/SEMB.2018.60352.Search in Google Scholar PubMed PubMed Central
[9] Temiz H, Özbek E, Gür Vural D, Özekinci T. Evaluation of antimicrobial resistance rates of Klebsiella isolates. Türk Mikrobiyol Cem Derg. 2015;45:68–74. 10.5222/TMCD.2015.068.Search in Google Scholar
[10] Zaman G, Jung IH, Torres DFM, Zeb A. Mathematical modeling and control of infectious diseases. Comput Math Methods Med. 2017;2017:7149154. 10.1155/2017/7149154.Search in Google Scholar PubMed PubMed Central
[11] Sultanoğlu N. Analysis of HIV epidemic in cyprus using a mathematical model. Erciyes Med J. 2021;44(1):63–7. 10.14744/etd.2021.32855.Search in Google Scholar
[12] Siettos CI, Russo L. Mathematical modeling of infectious disease dynamics. Virulence. 2013;4:295–306. 10.4161/viru.24041.Search in Google Scholar PubMed PubMed Central
[13] Sultanoglu N, Gokbulut N, Sanlidag T, Hincal E, Kaymakamzade B, Sayan M. A binomial model approach: Comparing the Ro Values of SARSCoV2 rRTPCR Data from Laboratories across Northern Cyprus. CMES. 2021;128:717–29. 10.32604/cmes.2021.016297.Search in Google Scholar
[14] Çetin E, Kiremitci B, Yurt İD. Mathematical Epidemiology: Pandemic A/H1N1 Case. Istanb Univ J Sch Bus Adm. 2009;38:197–209.Search in Google Scholar
[15] Işık N, Kaya A. Mathematical models and herd immunization for spreading and controlling of infectious diseases. Atatürk Üniv Vet Bil Derg. 2020;15:301–7. 10.17094/ataunivbd.715371.Search in Google Scholar
[16] FernandezMartinez JL, FernandezMuniz Z, Cernea A, Kloczkowski A. Predictive mathematical models of the shortterm and longterm growth of the COVID19 pandemic. Comput Math Methods Med. 2021;2021:5556433. 10.1155/2021/5556433.Search in Google Scholar PubMed PubMed Central
[17] van den Driessche P. Reproduction numbers of infectious disease models. Infect Dis Model. 2017;2:288–303. 10.1016/j.idm.2017.06.002.Search in Google Scholar PubMed PubMed Central
[18] Delamater PL, Street EJ, Leslie TF, Yang YT, Jacobsen KH. The complexity of the basic reproduction number (Ro). Emerg Infect Dis. 2019;25:1–4. 10.3201/eid2501.171901.Search in Google Scholar PubMed PubMed Central
[19] Baleanu D, Hassan Abadi M, Jajarmi A, Zarghami Vahid K, Nieto JJ. A new comparative study on the general fractional model of COVID19 with isolation and quarantine effects. Alex Eng J. 2022;61:4779–91. 10.1016/j.aej.2021.10.030.Search in Google Scholar
[20] Mustapha UT, Qureshi S, Yusuf A, Hincal E. Fractional modeling for the spread of Hookworm infection under Caputo operator. Chaos Solitons Fractals. 2020;137:109878. 10.1016/j.chaos.2020.109878.Search in Google Scholar
[21] Qureshi S, Jan R. Modeling of measles epidemic with optimized fractional order under Caputo differential operator. Chaos Solitons Fractals. 2021;145:110766. 10.1016/j.chaos.2021.110766.Search in Google Scholar
[22] Jajarmi A, Baleanu D, Zarghami Vahid K, Mobayen S. A general fractional formulation and tracking control for immunogenic tumor dynamics. Math Methods Appl Sci. 2022;45:667–80. 10.1002/mma.7804.Search in Google Scholar
[23] Bagkur C, Guler E, Kaymakamzade B, Hincal E, Suer K. Near future perspective of ESBLProducing Klebsiella pneumoniae strains using mathematical modeling. CMES. 2022;130:111–32. 10.32604/cmes.2022.016957.Search in Google Scholar
[24] TRNC State Planning Organization. Turkish Republic of Northern Cyprus Statistical Year Book 2018 Prime Ministry State Planning Organization Statistics and Research Department; 2018. http://www.devplan.org/Ecosos/Book/SEG2018.pdf (Accessed: 14 December 2021).Search in Google Scholar
[25] Cantas L, Suer K, Guler E, Imir T. High emergence of ESBLproducing E. coli Cystitis: time to get smarter in Cyprus. Front Microbiol. 2016;6:1446. 10.3389/fmicb.2015.01446.Search in Google Scholar PubMed PubMed Central
© 2022 Ulas Hurdoganoglu et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.