Structures and Electron Transport Paths in the Four Families of Flavin-Based Electron Bifurcation Enzymes.

Oxidoreductases facilitating electron transfer between molecules are pivotal in metabolic pathways. Flavin-based electron bifurcation (FBEB), a recently discovered energy coupling mechanism in oxidoreductases, enables the reversible division of electron pairs into two acceptors, bridging exergonic and otherwise unfeasible endergonic reactions. This chapter explores the four distinct FBEB complex families and highlights a decade of structural insights into FBEB complexes. In this chapter, we discuss the architecture, electron transfer routes, and conformational changes across all FBEB families, revealing the structural foundation that facilitate these remarkable functions.

Modeling and analysis of a human papilloma virus transmission model with impact of media.

The human papillomavirus (HPV) is threatening human health as it spreads globally in varying degrees. On the other hand, the speed and scope of information transmission continues to increase, as well as the significant increase in the number of HPV-related news reports, it has never been more important to explore the role of media news coverage in the spread and control of the virus. Using a decreasing factor that captures the impact of media on the actions of people, this paper develops a model that characterizes the dynamics of HPV transmission with media impact, vaccination and recovery. We obtain global stability of equilibrium points employing geometric method, and further yield effective methods to contain the HPV pandemic by sensitivity analysis. With the center manifold theory, we show that there is a forward bifurcation when R0=1. Our study suggested that, besides controlling contact between infected and susceptible populations and improving effective vaccine coverage, a better intervention would be to strengthen media coverage. In addition, we demonstrated that contact rate and the effect of media coverage result in multiple epidemics of infection when certain conditions are met, implying that interventions need to be tailored to specific situations.

Percutaneous coronary intervention involving coronary bifurcation is associated with higher mortality and complications.

BACKGROUND: Percutaneous coronary intervention (PCI) in patients with bifurcation lesions is associated with higher complexity and adverse outcomes. The goal of this study was to evaluate the inpatient outcomes of patients with PCI of bifurcation lesions. METHODS: The National Inpatient Sample (NIS) database, years 2016-2020, was studied using ICD 10 codes. Patients undergoing PCI for bifurcation lesions were compared to those undergoing PCI for non-bifurcation lesions, excluding chronic total occlusion lesions. We evaluated post-procedural inpatient mortality and complications. RESULTS: PCI in patients with bifurcation lesions was associated with higher mortality and post-procedural complications. A weighted total of 9,795,154 patients underwent PCI; of those, 43,480 had a bifurcation lesion. The bifurcation cohort had a 3.79% mortality rate, and the rate in those with non-bifurcation lesions was 2.56% (OR, 1.50; CI: 1.34-1.68; P<0.001). Upon conducting multivariate analysis, which adjusted for age, sex, race, and significant comorbidities, PCI for bifurcation lesions remained significantly associated with a higher mortality rate compared to non-bifurcation lesion PCI (OR, 1.68; 95% CI, 1.49-1.88; P<0.001). Furthermore, PCI for bifurcation lesions was associated with higher rates of myocardial infarction (OR, 2.26; 95% CI, 1.68-3.06; P<0.001), coronary perforation (OR, 7.97; 95% CI, 6.25-10.17; P<0.001), tamponade (OR, 3.46; 95% CI, 2.49-4.82; P<0.001), and procedural bleeding (OR, 5.71; 95% CI, 4.85-6.71; P<0.001). Overall, post-procedural complications were 4 times more in patients with bifurcation lesions than in those without (OR, 4.33; 95% CI, 3.83-4.88; P<0.001). CONCLUSION: Using a large, national inpatient database, we demonstrate that both mortality rates and post-procedural complication rates were significantly higher in patients undergoing PCI for bifurcation lesions than in those undergoing PCI for non-bifurcation lesions.

Gender-based disparities in outcomes of coronary bifurcation stenting in patients undergoing percutaneous coronary intervention: a systematic review and meta-analysis.

INTRODUCTION: Around 15-20% of lesions necessitating percutaneous coronary interventions (PCI) are attributed to coronary bifurcation lesions. We aim to study gender-based differences in PCI outcomes among bifurcation stents. METHODS: 3 studies were included after thorough systematic search using MEDLINE (EMBASE and PubMed). CRAN-R software using the Metabin module was used for statistical analysis. Pooled odds ratios (OR) were calculated using the random effect model and the Mantel-Haenszel method, with a 95% confidence interval (CI) used to determine statistical significance. Heterogeneity was assessed using Higgins I2. RESULT: Women exhibited a higher risk of in-hospital mortality (OR 0.67, 95% CI 0.58-0.76, I2 = 0%, P < 0.0001), post-procedural bleeding (OR 0.53, 95% CI 0.47-0.6, I2 = 0%, P < 0.0001) and post-procedure stroke (OR 0.72, 95% CI 0.52-1.0, I2 = 0%, P < 0.06) as compared to men. However, there were no significant differences in terms of myocardial infarction (OR 0.84, 95% CI 0.22-3.27, I2 = 49.4%, P < 0.80) and cardiac tamponade (OR 0.63, 95% CI 0.06; 5.72, I2 = 0%, P < 0.6821) in both groups. CONCLUSION: Our study reveals a noteworthy increase in in-hospital mortality in women, which could be attributed to a higher rate of major bleeding, advanced age, increased co-morbidities, and complex pathophysiology of the lesion in comparison to men. Further studies are required to gain a better understanding of the precise mechanisms thus enhancing procedural outcomes.

Multiple endemic equilibria in an environmentally-transmitted disease with three disease stages.

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R∗>1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R∗<1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R∗ appearing in this model are both responsible for the existence of endemic states.

Early effect of different bifurcation techniques on left ventricular mechanics in elective percutaneous coronary intervention.

BACKGROUND: Bifurcation lesions are prevalent amongst patients with symptomatic coronary artery disease subjected to percutaneous coronary intervention (PCI). Recent consensus commends a conservative (provisional) approach when managing the side branch. Here, the aim was to explore the immediate impact of different bifurcation techniques (one stent and two stent strategies) on left ventricular LV) myocardial functions using speckle tracking echocardiography in patients subjected to elective PCI. Sixty two consecutive patients diagnosed with coronary bifurcation lesion (CBL) were enrolled. Patients were categorized into: one-stent strategy (Provisional group, n = 44) and a two-stent strategy (TAP, DK crush, or Culotte technique, n = 18), based on the coronary bifurcation site, angle, side branch diameter and Medina classification. LVEF%, regional and global longitudinal strain (GLS), and E/E' were measured before and within 24 h post PCI. RESULTS: In both provisional and 2- stent technique, the mitral inflow velocities and mitral annular velocities showed improvement with significant reduction in E/e' (P < 0.03 and P < 0.001) respectively while LVEF% did not change. There were no significant changes in any other echo parameters post PCI. In provisional group, there were significant improvements in LAD (P < 0.001), RCA (P < 0.01) territories and GLS (P < 0.01). Δ LAD was expressively higher (34.5%) compared with Δ LCX (9.6%) and ΔRCA (25.4%), P < 0.001, P < 0.01 respectively. In the 2-stent technique group, there were significant improvements in peak longitudinal strain of LAD territory (P < 0.01), RCA territory (P < 0.01) and GLS (P < 0.01) respectively. Δ LAD territory was significantly higher in provisional group in comparison with the 2- stent technique group. Δ GLS was correlated inversely to Gensini score in provisional group and to the number of vessel diseased in 2-stent technique group. CONCLUSION: PCI of the bifurcation lesion positively impact myocardial function. Both bifurcation techniques improve LV mechanical properties using 2D strain imaging while LV EF% remains unchanged.

Investigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior.

This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system's behavior and the extent to which it deviates from the unperturbed case.

Coil embolization of the middle cerebral artery bifurcation aneurysms: Feasibility and durability.

OBJECTIVE: To evaluate the feasibility and durability of coil embolization for MCAB aneurysms by analyzing clinical and radiological results. METHODS: From January of 2008 to June of 2018, we treated a total of 1785 aneurysms using coil embolization. The aneurysms were treated by both coiling and stent-assisted coiling. Among these cases, 223 MCAB aneurysms were analyzed retrospectively. Clinical and radiological assessments were conducted at admission, after treatment, at discharge, and at last clinical follow-up. RESULTS: Coil embolization was performed on 223 MCAB aneurysms in 217 patients. Peri-procedural ischemic, hemorrhagic, and other complications within 30 days after coil embolization occurred at rates of 8.0 %, 8.0 %, and 2.0 %, respectively, in the ruptured group and at 2.9 %, 1.2 %, and 0 %, respectively, in the unruptured group. The overall morbidity and mortality rates associated with complications were 2.3 % and 2.0 %. The cumulative major recurrence rates were 5.1 % at 12 months, 7.1 % at 18 months, and 11.9 % at three years after coil embolization. The mean follow-up period was 33.27 ± 25.48 months. Independent risk factors for major recurrence after coil embolization for MCAB aneurysms were a ruptured aneurysm, initial incomplete occlusion, the aneurysm size, and the neck size. CONCLUSION: Coil embolization is a good alternative treatment option for MCAB aneurysms compared to surgical clipping. Considering the risk factors for major recurrence, the follow-up angiography should continue up to three years after coil embolization.

Disruption of the creb3l1 gene causes defects in caudal fin regeneration and patterning in zebrafish Danio rerio.

BACKGROUND: The gene cAMP-Responsive Element Binding protein 3-like-1 (CREB3L1) has been implicated in bone development in mice, with CREB3L1 knock-out mice exhibiting fragile bones, and in humans, with CREB3L1 mutations linked to osteogenesis imperfecta. However, the mechanism through which Creb3l1 regulates bone development is not fully understood. RESULTS: To probe the role of Creb3l1 in organismal physiology, we used CRISPR-Cas9 genome editing to generate a Danio rerio (zebrafish) model of Creb3l1 deficiency. In contrast to mammalian phenotypes, the Creb3l1 deficient fish do not display abnormalities in osteogenesis, except for a decrease in the bifurcation pattern of caudal fin. Both, skeletal morphology and overall bone density appear normal in the mutant fish. However, the regeneration of caudal fin postamputation is significantly affected, with decreased overall regenerate and mineralized bone area. Moreover, the mutant fish exhibit a severe patterning defect during regeneration, with a significant decrease in bifurcation complexity of the fin rays and distalization of the bifurcation sites. Analysis of genes implicated in bone development showed aberrant patterning of shha and ptch2 in Creb3l1 deficient fish, linking Creb3l1 with Sonic Hedgehog signaling during fin regeneration. CONCLUSIONS: Our results uncover a novel role for Creb3l1 in regulating tissue growth and patterning during regeneration.

Exploring chaos and bifurcation in a discrete prey-predator based on coupled logistic map.

This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system's behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic behavior is analyzed using Marotto's approach. The OGY feedback control method is implemented to control chaos. Theoretical findings are validated through numerical simulations.

Bifurcation detection in intravascular optical coherence tomography using vision transformer based deep learning.

Objective. Bifurcation detection in intravascular optical coherence tomography (IVOCT) images plays a significant role in guiding optimal revascularization strategies for percutaneous coronary intervention (PCI). We propose a bifurcation detection method using vision transformer (ViT) based deep learning in IVOCT.Approach. Instead of relying on lumen segmentation, the proposed method identifies the bifurcation image using a ViT-based classification model and then estimate bifurcation ostium points by a ViT-based landmark detection model.Main results. By processing 8640 clinical images, the Accuracy and F1-score of bifurcation identification by the proposed ViT-based model are 2.54% and 16.08% higher than that of traditional non-deep learning methods, are similar to the best performance of convolutional neural networks (CNNs) based methods, respectively. The ostium distance error of the ViT-based model is 0.305 mm, which is reduced 68.5% compared with the traditional non-deep learning method and reduced 24.81% compared with the best performance of CNNs based methods. The results also show that the proposed ViT-based method achieves the highest success detection rate are 11.3% and 29.2% higher than the non-deep learning method, and 4.6% and 2.5% higher than the best performance of CNNs based methods when the distance section is 0.1 and 0.2 mm, respectively.Significance. The proposed ViT-based method enhances the performance of bifurcation detection of IVOCT images, which maintains a high correlation and consistency between the automatic detection results and the expert manual results. It is of great significance in guiding the selection of PCI treatment strategies.

A mathematical model of mobility-related infection and vaccination in an epidemiological case.

In this study, we established a system of differential equations with piecewise constant arguments to explain the impact of epidemiological transmission between different locations. Our main goal is to look into the need for vaccines as well as the necessity of the lockdown period. We proved that keeping social distance was necessary during the pandemic spread to stop transmissions between different locations and that re-vaccinations, including screening tests, were crucial to avoid reinfections. Using the Routh-Hurwitz Criterion, we examined the model's local stability and demonstrated that the system could experience Stationary and Neimark-Sacker bifurcations depending on certain circumstances.

Modeling a SEIVRS dynamic behavior with transportation-related transmissionEstablishing a system of two urban as differential equations with piecewise constant argumentsStability analysis of disease-free and co-existing equilibrium pointsAnalyzing bifurcation types around the disease-free and co-existing equilibrium points.Illustrating numerical scenarios that were applied during the pandemic event.

Fractional-order Sprott K chaotic system and its application to biometric iris image encryption.

Fractional-order (FO) chaotic systems exhibit random sequences of significantly greater complexity when compared to integer-order systems. This feature makes FO chaotic systems more secure against various attacks in image cryptosystems. In this study, the dynamical characteristics of the FO Sprott K chaotic system are thoroughly investigated by phase planes, bifurcation diagrams, and Lyapunov exponential spectrums to be utilized in biometric iris image encryption. It is proven with the numerical studies the Sprott K system demonstrates chaotic behaviour when the order of the system is selected as 0.9. Afterward, the introduced FO Sprott K chaotic system-based biometric iris image encryption design is carried out in the study. According to the results of the statistical and attack analyses of the encryption design, the secure transmission of biometric iris images is successful using the proposed encryption design. Thus, the FO Sprott K chaotic system can be employed effectively in chaos-based encryption applications.

The impact of the Woven EndoBridge device on the treatment of anterior circulation wide-neck bifurcation aneurysms: a single-center experience.

OBJECTIVE: The paucity of literature comparing Woven EndoBridge (WEB) embolization to microsurgical clipping for anterior circulation wide-neck bifurcation aneurysms (WNBAs) underscores the need for further investigation into the optimal management of this patient subpopulation. The objective of this study was to compare the rate of endovascular and microsurgical treatment of WNBAs before and after the introduction of the WEB device. In addition, the authors performed a comparison of demographics, aneurysm characteristics, and treatment outcomes in patients before and after the introduction of the WEB device. METHODS: This study was a retrospective review of the usage rate of different treatment modalities for WNBAs before and after the WEB device was approved by the US FDA on September 27, 2018. RESULTS: The study cohort comprised 235 patients with anterior circulation WNBAs treated at the authors' institution, including 127 aneurysms treated pre-WEB and 108 treated post-WEB. Generally, the rate of endovascular treatment of anterior circulation WNBAs was significantly higher post-WEB (86.1% vs 46.5%, p < 0.001), while the rate of clipping was significantly lower (13.9% vs 53.5%, p < 0.001). During follow-up, the rate of adequate aneurysm occlusion (Raymond-Roy occlusion classification [RROC] grades 1 and 2) was nonsignificantly higher in the post-WEB cohort (83.9% vs 78.5%, p = 0.34), while the rate of RROC grade 3 was nonsignificantly higher in the pre-WEB cohort (21.5% vs 16.1%, p = 0.34). Additionally, and although nonsignificant, the rates of recurrence (pre-WEB 25.3% vs post-WEB 14.9%, p = 0.12) and retreatment (pre-WEB 22.8% vs post-WEB 14.9%, p = 0.22) were higher in the pre-WEB cohort. Recurrence was assessed before retreatment. CONCLUSIONS: After the introduction of the WEB device, the rate of endovascular treatment of WNBAs increased while the rate of microsurgical clipping decreased. It is essential for neurointerventionalists to become familiar with the indications, advantages, and shortcomings of all these different techniques to be able to match the right patient with the right technique to produce the best outcome.

A bypass flow model to study endothelial cell mechanotransduction across diverse flow environments.

Disturbed flow is one of the pathological initiators of endothelial dysfunction in intimal hyperplasia (IH) which is commonly seen in vascular bypass grafts, and arteriovenous fistulas. Various in vitro disease models have been designed to simulate the hemodynamic conditions found in the vasculature. Nonetheless, prior investigations have encountered challenges in establishing a robust disturbed flow model, primarily attributed to the complex bifurcated geometries and distinctive flow dynamics. In the present study, we aim to address this gap by introducing an in vitro bypass flow model capable of inducing disturbed flow and other hemodynamics patterns through a pulsatile flow in the same model. To assess the model's validity, we employed computational fluid dynamics (CFD) to simulate hemodynamics and compared the morphology and functions of human umbilical venous endothelial cells (HUVECs) under disturbed flow conditions to those in physiological flow or stagnant conditions. CFD analysis revealed the generation of disturbed flow within the model, pinpointing the specific location in the channel where the effects of disturbed flow were observed. High-content screening, a single-cell morphological profile assessment, demonstrated that HUVECs in the disturbed flow area exhibited random orientation, and morphological features were significantly distinct compared to cells in the physiological flow or stagnant condition after a two days of flow exposure. Furthermore, HUVECs exposed to disturbed flow underwent extensive remodeling of the adherens junctions and expressed higher levels of endothelial cell activation markers compared to other hemodynamic conditions. In conclusion, our in vitro bypass flow model provides a robust platform for investigating the associations between disturbed flow pattern and vascular diseases.

Percutaneous coronary intervention for unprotected left main distal bifurcation lesions in elderly people.

BACKGROUND: In the elderly people with unprotected left main distal bifurcation lesions (ULMD), percutaneous coronary intervention (PCI) is often selected as first choice treatment strategy because of perioperative high risk of coronary artery bypass graft surgery due to their large number of comorbidities. Also, some recent papers reported that geriatric nutritional risk index (GNRI) is also strongly associated with clinical outcomes after interventional procedures in elderly patients. OBJECTIVES: We assessed clinical outcomes after PCI for ULMD and the impact of GNRI in elderly patients. METHODS: We identified 669 non dialysis patients treated with current generation drug-eluting stent for ULMD from MITO registry. We divided the patients to the following 2 groups; elderly group (n = 240, age ≥75) and young group (n = 429, age <75). Additionally, we could calculate GNRI and divided elderly group into 2 group based on the median value of the GNRI. The primary endpoint was all-cause mortality. RESULTS: All-cause mortality was significantly higher in elderly group [adjusted hazard ratio (HR) 2.37; 95% confidence interval (CI), 1.40-4.02; p = 0.001]. All-cause mortality was significantly higher in low GNRI elderly group compared to other 2 groups (Adjusted HR of elderly with low GNRI: 3.56, 95%CI (1.77-7.14), p < 0.001). Cardiovascular mortality was comparable between two groups. TLR rate was significantly lower in elderly group (adjusted HR 0.57; 95% CI, 0.34-0.97; p = 0.035). CONCLUSIONS: The elderly had higher all-cause mortality after PCI for ULMD compared to young people. Especially, the elderly with low GNRI were extremely associated with poorer outcomes.

Laparoscopic Resection of Para-Aortic Mass at the Aortic Bifurcation: An Atypical Presentation of a Tailgut Cyst.

We review the case of a 43-year-old white male who presented with an enlarging pulsatile mass in the periumbilical region. Diagnostic imaging revealed an 8-cm heterogeneous mass abutting the left iliac artery at the aortic bifurcation. Due to the patient's persistently elevated blood pressure and elevated serum and urine catecholamines, a neuroendocrine tumor was suspected. Laparoscopic resection was performed and was well tolerated. However, the mass was characterized as a tailgut cyst upon pathological examination. This case highlights the utility of laparoscopy for the removal of large para-aortic masses, which can be achieved in a safe fashion by an experienced surgeon. In addition, this case highlights the importance of differential diagnoses in surgeries due to the occurrence of unexpected outcomes.

Left anterior descending coronary artery-left circumflex coronary artery bifurcation angle and severity of coronary artery disease; is there any correlation? A cross-sectional study.

Background and Aims: The aim of this study is to evaluate the association of coronary computed tomography angiography derived (CCTA) plaque characteristics and the left anterior descending coronary artery (LAD) and left circumflex coronary artery (LCX) bifurcation angle with severity of coronary artery disease (CAD). Methods: All the stable patients with suspected CAD who underwent CCTA between January to December 2021 were included. Correlation between CCTA-derived aggregated plaque volume (APV), LAD-LCX angle, remodeling index (RI), coronary calcium score with Gensini score in conventional angiography were assessed. One hundred and twenty-two patients who underwent both CCTA and coronary angiography were analyzed. Results: Our analysis showed that the median (percentile 25% to percentile 75%) of the APV, LAD-LCx angle, and calcium score were 31% (17%-47%), 58° (39°-89°), and 31 (0-186), respectively. Also, the mean ± SD of the RI was 1.05 ± 0.20. Significant correlation between LAD-LCx bifurcation angle (0.0001-0.684), APV (0.002-0.281), RI (0.0001-0.438), and calcium score (0.016-0.217) with Gensini score were detected. There was a linear correlation between the mean LAD-LCx bifurcation angle and the Gensini score. The sensitivity and specificity for the cut-off value of 47.5° for the LAD-LCX angle were 86.7% and 82.1%, respectively. Conclusion: There is a direct correlation between the LAD-LCx angle and the Gensini score. In addition to plaque characteristics, anatomic-based CCTA-derived indices can be used to identify patients at higher risk for CAD.

Global analysis of a diffusive Cholera model with multiple transmission pathways, general incidence and incomplete immunity in a heterogeneous environment.

With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.