Computer Modeling in Engineering & Sciences |

DOI: 10.32604/cmes.2022.016957

ARTICLE

Near Future Perspective of ESBL-Producing Klebsiella pneumoniae Strains Using Mathematical Modeling

1Department of Medical Microbiology and Clinical Microbiology, Near East University, Nicosia, 99010, Cyprus

2Department of Nutrition and Dietetics, Near East University, Nicosia, 99010, Cyprus

3DESAM Institute, Near East University, Nicosia, 99010, Cyprus

4Department of Mathematics, Near East University, Nicosia, 99010, Cyprus

5Mathematics Research Center, Near East University, Nicosia, 99010, Cyprus

6Department of Infectious Diseases and Clinical Microbiology, Near East University, Nicosia, 99010, Cyprus

*Corresponding Author: Cemile Bagkur. Email: cemilebagkur@hotmail.com

Received: 14 April 2021; Accepted: 12 July 2021

Abstract: While antibiotic resistance is becoming increasingly serious today, there is almost no doubt that more challenging times await us in the future. Resistant microorganisms have increased in the past decades leading to limited treatment options, along with higher morbidity and mortality. Klebsiella pneumoniae is one of the significant microorganisms causing major public health problems by acquiring resistance to antibiotics and acting as an opportunistic pathogen of healthcare-associated infections. The production of extended spectrum beta-lactamases (ESBL) is one of the resistance mechanisms of K. pneumoniae against antibiotics. In this study, the future clinical situation of ESBL-producing K. pneumoniae was investigated in order to reflect the future scenarios to understand the severity of the issue and to determine critical points to prevent the spread of the ESBL-producing strain. For evaluation purposes, SIS-type mathematical modeling was used with retrospective medical data from the period from 2016 to 2019. Stability of the disease-free equilibrium and basic reproduction ratios were calculated. Numerical simulation of the SIS model was conducted to describe the dynamics of non-ESBL and ESBL-producing K. pneumoniae. In order to determine the most impactful parameter on the basic reproduction ratio, sensitivity analysis was performed. A study on mathematical modeling using data on ESBL-producing K. pneumoniae strains has not previously been performed in any health institution in Northern Cyprus, and the efficiency of the parameters determining the spread of the relevant strains has not been investigated. Through this study, the spread of ESBL-producing K. pneumoniae in a hospital environment was evaluated using a different approach. According to the study, in approximately seventy months, ESBL-producing K. pneumoniae strains will exceed non-ESBL K. pneumoniae strains. As a result, the analyses showed that hospital admissions and people infected with non-ESBL or ESBL-producing K. pneumoniae have the highest rate of spreading the infections. In addition, it was observed that the use of antibiotics plays a major role in the spread of ESBL-producing K. pneumoniae compared to other risk factors such as in-hospital transmissions. As a matter of course, recoveries from Klebsiella infections were seen to be the most effective way of limiting the spread. It can be concluded from the results that although the use of antibiotics is one of the most effective factors in the development of the increasing ESBL-producing K. pneumoniae, regulation of antibiotic use policy could be a remedial step together with effective infection control measures. Such steps may hopefully lead to decreased morbidity and mortality rates as well as improved medical costs.

Keywords: Mathematical modeling; Klebsiella pneumoniae; extended spectrum beta lactamases (ESBL)

Klebsiella pneumoniae (K. pneumoniae) is a member of the Enterobacteriaceae family, which is a saprophyte found in the gastrointestinal tract of humans. It is an opportunistic pathogen that causes complicated and difficult to treat community-acquired and nosocomial infections such as in the urinary system, soft tissue, pneumonia and bacteremia, and usually affects immunosuppressive and in-patients [1,2]. The increase in antibiotic-resistant K. pneumoniae species has caused outbreaks in hospitals in many countries, leading to high mortality rates in infected people [3].

The problem of antibiotic resistance is a major obstacle for clinicians, veterinarians and other infection control workers in the treatment and prevention of microorganisms that cause infections [4]. The most important mechanism of resistance seen in Klebsiella species is the production of extended spectrum beta-lactamase (ESBL). Carbapenem group antibiotics are the first choice agents in the treatment of infections caused by ESBL-producing gram-negative bacteria. As a result of the the widespread and improper use of carbapenems, resistance problems have arisen against this group of antibiotics. Outbreaks and sporadic cases caused by K. pneumoniae species producing ESBL and carbapenemase in all health institutions, especially in intensive care units, have been escalating with an increasing incidence rate around the world in recent years, which has led to global concern [1–5]. Many factors such as increased antimicrobial resistance, increased human interactions and dynamic human behavior have affected the prevention and control of infectious diseases, causing them to become international problems rather than just national issues. Against this complexity, mathematical models provide the necessary tools to synthesize information to understand epidemiological patterns and to develop the quantitative evidence base for making global health decisions. Mathematical models in epidemiology provide an insight into the underlying mechanisms that affect the spread of disease at the population level [6]. To help understand and control infectious diseases, mathematical models are increasingly being used, particularly to identify key parameters leading to disease spread, evaluate the impact of potential interventions, and predict the trajectory of outbreaks. Although the role of mathematical modeling in the control of emerging infections can be clearly observed, it is thought that it can be an effective tool in antimicrobial resistance control [7]. The studies conducted by Lipsitch et al. and Weinstein et al. [8,9] also support the idea that mathematical modeling can be useful for the investigation of antibiotic resistance of nosocomial pathogens.

In infectious diseases, the frequency of causative microorganisms and their antibiotic sensitivity can change over time. Therefore, in order to guide empirical treatment, changes in the active microorganism and antibiotic susceptibility should be determined by each institution. Correct determination of policies for use of antibiotics is critical in identifying the appropriate treatment and preventing the development of resistance [10].

Considering that 30 years have passed since the emergence of a new class of antibiotics, the treatment of resistant strains with new drugs seems unlikely to succeed. Taking precautions to prevent the increasing spread of resistance rather than waiting for new antibiotic classes is the most effective step that can be taken. For this reason, the rates of non-ESBL and ESBL-producing strains of K. pneumoniae over the years are calculated using mathematical modeling. The data used in the study are cumulative data of K. pneumoniae from 2016 to 2019. The aim is to determine the future distribution of non-ESBL and ESBL-producing K. pneumoniae strains in the hospital and to identify possible future problems in order to prevent them with the measures taken today.

Consequently, for the improvement of treatment options, reduction of medical costs and decrease of morbidity and mortality rates of resistant microorganisms, precautions must be taken and it is necessary to regulate the use of antibiotics and raise awareness on resistance.

Using mathematical models to predict outcomes in the medical field is helpful for clinicians as this practice enables our knowledge to be expanded further based on actual data. Limitations such as repeating studies, possible risks and researching on actual patients can be overcome. As nonlinear systems are inherently unpredictable, mathematical modeling can be used in the medical field, such as to describe the performance of an organ or to investigate the behavior of an organ system [11,12]. Therefore, mathematical modeling plays an important role in understanding many complex biological systems and investigating global events such as pandemics in detail [13].

As the spread of ESBL-producing K. pneumoniae is a global threat, investigations to determine the hospital departments in which it is more common and detailed examinations of clonal diversity through molecular genotyping have been performed by many researchers [14,15]. Control measures and public health interventions have also been evaluated through mathematical models [16,17]. This study shows what will await us in the future regarding ESBL-producing K.pneumoniae infections if the current situation continues and how much time remains for the worst-case scenario in which the ESBL-producing strains exceed the non-ESBL strains.

To the best of our knowledge, the present study is the first to examine data on ESBL-producing K. pneumoniae using mathematical modeling in a health institution in Northern Cyprus. By the means of numerical simulations and sensitivity analysis, we can predict what expects us in an estimated time and what are the significant parameters in terms of preventing increases in the rates of morbidity and mortality. The contribution of effective parameters in the infection process is also enlightened with the possibilities offered by mathematical modeling, and the study, which was carried out with the joint work of two different fields, sets an example in terms of the importance of a multidisciplinary approach in infection control.

The main contributions of this research can be summarized as follows: by using an SIS-type model, the dynamics of the non-ESBL and ESBL-producing K. pneumoniae strains for the near future were analyzed and the effects of these dynamics were discussed. Sensitivity analysis was performed to determine the effect of important parameters on the basic reproduction ratio for both non-ESBL and ESBL-producing K. pneumoniae strains.

The remainder of the article proceeds as follows. In Section 2, collected K. pneumoniae data are adapted to a SIS-type model. In Section 3, the values of the model in numerical simulation and sensitivity analysis are specified. In the last sections, a discussion of the results and concluding remarks are presented.

2.1 Collection of Klebsiella Data

Klebsiella spp. strains detected in patients who presented to the university hospital between 2016 and 2019 were determined by selecting certain parameters from the hospital data system. In addition to parameters such as age, gender, culture samples (e.g., urine, sputum, aspirate), and relevant departments (e.g., intensive care, infection, internal medicine), the strains were also grouped according to whether they were ESBL positive (ESBL-producing) or ESBL negative (non-ESBL). The obtained data were evaluated by the mathematics department for mathematical modeling.

2.2 Identification and Antimicrobial Susceptibility Tests of Klebsiella Strains

Culture samples were delivered to the microbiology laboratory of the university hospital. The samples were inoculated on blood and eosin methylene blue (EMB) media then incubated at 35°C for 24–48 h. Specimens with gram-negative growth were prepared in 0.5 McFarland bacterial suspension in accordance with the manufacturer's recommendations. Prepared suspensions were loaded into a BD Phoenix™ 100 device for identification and analysis of antimicrobial susceptibility tests.

2.3 Mathematical Adaptation of the Collected Data to a Model

2.3.1 Mathematical Model of Klebsiella pneumoniae

In the SIS-type model, populations within the hospital are stated in three mutually exclusive ways: susceptible

The rate that individuals enter the hospital infected with ESBL- is

2.3.2 Stability of Disease Free Equilibrium Point (DFE) and Basic Reproduction Ratio

By equalizing each equation in the system (1) to zero and with the assumption

Using the next generation matrix method,

then the basic reproduction number (

Theorem 1: For the model (1), the disease-free equilibrium (2) is locally asymptotically stable whenever

Proof:

The Jacobian matrix at the DFE point of the model (1):

The eigenvalues of the Jacobian matrix are

In this section, numerical results are calculated by simulating the model using the real data obtained the university hospital for the period 2016 and 2019. The model parameters used for this simulation are: S,

2.3.4 Sensitivity Analysis of

The sensitivity analysis was used to understand the sensitivity of the basic reproduction number in relation to the important parameters used throughout the model. The computation of the expression of the basic reproduction number was carried out in Section 2.3.2 above and is denoted by

The computation of the normalized local sensitivity indices of R0 proportional to the parameters was performed. Here, the set of input parameters relative to R0 are

We denoted R0 by the normalized local sensitivity index with respect to a parameter found in

Using the above definition in (5), we computed the following indices (6)–(15) for the output R0 with respect to every parameter presented in.

3.1 Mathematical Model of Klebsiella pneumoniae

In this paper, we studied an SIS-type model. The model shown in Fig. 1 demonstrates the transmission dynamics of Klebsiella bacteria with the acquisition of non-ESBL (

3.2 Numerical Simulation and Basic Reproduction Ratio

By simulating the model, the values of the parameters calculated based on the data are presented in Table 2.

Basic reproduction numbers

Basic reproduction ratios of

Since both

3.3 Sensitivity Analysis of

We used local sensitivity analysis to illustrate the impact of each model parameter on

Table 3 demonstrates that increasing (respectively decreasing) any rate

The present study was carried out to evaluate the spread of non-ESBL and ESBL-producing K. pneumoniae strains in the hospital environment for the following years. In this context, based on the transmission dynamics of K. pneumoniae, an SIS-type model was created. Basic reproduction numbers

The basic reproduction number (R0) is the measurement of the potential of a disease to spread in a given population. If a disease is introduced to a population by an infected individual in the absence of immunity to the particular disease, the subsequent generation of secondary cases is defined as R0 [18].

R0 < 1 is described as the situation where an infected individual can cause less than one new case on average during the individual's infection period. Then, the infection will die out and not spread. In this case, the disease free equilibrium is locally asymptotically stable. On the other hand, R0 > 1 is described as being when any infected individual can cause more than one new case on average so that the infection will be able to spread, indicating the possibility of an endemic. In this situation, the disease free equilibrium is locally asymptotically unstable [19].

According to the model parameters, which were calculated from the data collected from the hospital,

Even though the

Numerical results were calculated by simulating the model using real data obtained from the university hospital between the years of 2016 and 2019. The dynamics of non-ESBL and ESBL-producing strains are shown in Fig. 2. According to the table, at the present time, the number of ESBL-producing strains is less than non-ESBL strains. However, as time progresses, the ESBL-producing strain number approaches the number of non-ESBL strains in the fortieth month. From this point, the lines of ESBL-producing strains and non-ESBL strains seem to continue almost equally for thirty months. By the seventieth month, ESBL-producing strains start to increase gradually leaving the non-ESBL strains behind. This table shows that in forty months, ESBL-producing strains will arise, thus causing antibiotic resistance and difficulties in the treatment of resistant pathogens. In addition, as the treatment will be challenging, morbidity and mortality rates will also increase together with treatment costs. For two and a half years, while the rates of non-ESBL and ESBL-producing strains are expected to be equivalent, almost 6 years later, infections caused by ESBL-producing K. pneumoniae strains will exceed non-ESBL K. pneumoniae infections. To avoid such a situation, strict precautions must be taken by the hospital's infection control committee to prevent the spread of ESBL-producing strains. It is important that health-care workers are educated on how to take care of patients infected or colonized with ESBL-producing K. pneumoniae. Sanitation, disinfection and sterilization must be properly applied to these patients’ rooms and medical devices. Antimicrobial susceptibility tests must be performed to follow the resistance profiles of patients for efficient therapeutic applications.

A study carried out by Navon-Venezia et al. in 2017 produced a similar table showing that between 2005 and 2015, the resistance rates of K. pneumoniae steadily increased over the years. The study was carried four antibiotic classes including the third-generation cephalosporins, aminoglycosides, fluoroquinolones and carbapenems, and it was found that the resistance rates between countries varied [24].

In the case of the spread of an infection, in order to determine which parameter and at what magnitude would be the most effective in reducing the R0 value, sensitivity analysis is used. Determination of control measures informs the infection control committee which points require more attention. In this study, all increases were made at 10% for sensitivity analysis of the model. Increasing the rates of hospital admissions (

As an opportunistic pathogen, K. pneumoniae accounts for one third of all gram-negative infections causing urinary tract infections, pneumonia, wound infections, intra-abdominal infections and septicemia [24]. In addition, Klebsiella plays a role in community-acquired infections such as necrotizing pneumonia, pyogenic liver abscesses and endogenous endophthalmitis [23]. It is among the top three most causative agents of neonatal sepsis in most facilities [25]. ESBL-producing and carbapenem-resistant K. pneumoniae is accepted as a critical public health threat by the World Health Organization (WHO) that accounts for >90,000 infections with >7,000 deaths in Europe on an annual basis [26,27]. This high rate and the variety of infections certainly contribute to increased R0 values. Besides being a nosocomial pathogen, it can exhibit wide phenotypic and genetic diversity, as it can be found in many environmental and host-associated niches [28]. This increases the ease by which Klebsiella infections can be acquired.

The administration of any drug (

As fluoroquinolones are broad-spectrum antibiotics, they were extensively used for empirical treatment of infections caused by gram-negative bacteria. Also, it was found that ESBLs frequently mediate the mechanisms of resistance to fluoroquinolones [29]. Accordingly, fluoroquinolone resistance emerged, thus making third-generation cephalosporins the choice of empirical treatment. Unfortunately, for the treatment of community-associated or healthcare-associated infections, ESBL-producing strains displayed resistance to third-generation cephalosporins [30]. Accordingly, for the treatment of non-ESBL infections, empirical treatment options must be chosen carefully. Regional patterns of resistance for community-associated infections and risk factors for patients in terms of acquiring resistance to third-generation cephalosporins must be considered. Another study carried out by Salzar-Vizcaya et al. in 2019 showed that public health interventions aimed at reducing antimicrobial consumption were observed to effectively reduce the prevalence of ESBL-producing K. pneumoniae [17]. The usage of antibiotics can lead to selective pressure by killing susceptible bacteria and allowing resistant bacteria to survive and then multiply. Hence, while treating non-ESBL infections, selective antimicrobial pressure should be avoided. For the treatment of ESBL-producing infections, choosing the proper drug is crucial, while the dosage and duration should be followed according to the severity of the illness.

Sensitivity analysis also showed that increasing the transmission rate from non-ESBL K. pneumoniae to susceptible individuals (

Increasing the transmission rate from non-ESBL strains to ESBL-producing strains (

The present study is the first to examine data on ESBL-producing K. pneumoniae using mathematical modeling in a health institution in Northern Cyprus. The contribution of effective parameters in the infection process was also enlightened with the possibilities offered by mathematical modeling, and the study, which was carried out with the joint work of two different fields, sets an example in terms of the importance of the multidisciplinary approach in infection control. To summarize, it seems clear that the use of antibiotics has a 6-times greater effect in the formation of the ESBL-producing K. pneumoniae strains compared to other factors such as in-hospital transmissions, horizontal gene transfers or mutations. Although antibiotics are seen as a remedy in the treatment of infections, negligent use of antibiotics can cause the phenomenon of resistance, which may cause medical treatment to return to the period before antibiotics were available. Hence, the study suggests that, as there is no new class of antimicrobial agents, existing ones should be used efficiently. The local population's resistance rates should be considered while using empiric therapy. Over-the-counter sales of antibiotics still exist in many parts of the world, which carries the possibility of causing resistance to antibiotics. The sale of antibiotics without medical prescription can lead to the occurrence of community-acquired ESBL infections. As it is already challenging to treat ESBL infections, the rational use of drugs, the choice of the right drug and adjustment of dosage, duration and administration are vital. Combination therapies should be considered using drugs that have a synergistic effect to prevent the formation of resistance. In cases where ESBL positive infections are present, the infection control committee must take appropriate measures in terms of both personnel and technical aspects in order to minimize in-hospital transmissions. Surveillance studies are very important in infection control. By obtaining more precise data with mathematical modeling, surveillance of the relevant strain can be conducted more effectively. In line with the data obtained, it seems necessary to take urgent measures. Through the regulation of antibiotic use policy and training of hospital staff about how to handle with resistance microorganisms, high morbidity and mortality rates can be prevented and the treatment of resistant infections can be improved. Therefore, it is believed that this will prevent the enormous increase in ESBL-producing K. pneumoniae infections over time, and will provide both therapeutic and financial improvements in the medical field. In order to extend the presented research, as a future recommendation, control strategies can be created to observe changes in the spread of ESBL-producing K. pneumoniae in the hospital using fractional models [33]. Fractional differential equations (FDEs) or delay differential equations (DDEs) can be used to examine and compare the subject with different approaches.

Limitations: The study has been conducted by ignoring death from Klebsiella pneumoniae infection.

Funding Statement: The authors received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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