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In this work, we employed an attractive hybrid integral transform technique known as the natural transform decomposition method (NTDM) to investigate analytical solutions for the Noyes-Field (NF) model of the time-fractional Belousov-Zhabotinsky (TF-BZ) reaction system. The aforementioned time-fractional model is considered within the framework of the Caputo, Caputo-Fabrizio, and Atangana-Baleanu fractional derivatives. The NTDM couples the Adomian decomposition method and the natural transform method to generate rapidly convergent series-type solutions via an elegant iterative approach. The existence and uniqueness of solutions for the considered time-fractional model are first investigated via a fixed-point approach. The reliability and efficiency of the considered solution method is then demonstrated for two test cases of the TF-BZ reaction system. To demonstrate the validity and accuracy of the considered technique, numerical results with respect to each of the mentioned fractional derivatives are presented and compared with the exact solutions as well as with those from existing related literature. Graphical representations depicting the dynamic behaviors of the chemical wave profiles of the concentrations of the intermediates are presented with respect to varying fractional parameter values as well as temporal and spatial variables. The obtained results indicate that the execution of the method is straightforward and can be employed to explore nonlinear time-fractional systems modeling complex chemical reactions., (© 2024. The Author(s).)

Solitary wave solutions are of great interest to bio-mathematicians and other scientists because they provide a basic description of nonlinear phenomena with many practical applications. They provide a strong foundation for the development of novel biological and medical models and therapies because of their remarkable behavior and persistence. They have the potential to improve our comprehension of intricate biological systems and help us create novel therapeutic approaches, which is something that researchers are actively investigating. In this study, solitary wave solutions of the nonlinear Murray equation will be discovered using a modified extended direct algebraic method. These solutions represent a uniform variation in blood vessel shape and diameter that can be used to stimulate blood flow in patients with cardiovascular disease. These solutions are newly in the literature, and give researchers an important tool for grasping complex biological systems. To see how the solitary wave solutions behave, graphs are displayed using Matlab., (© 2024. The Author(s).)

The aim of this study is to analyze and investigate the SARS-CoV-2 (SC-2) transmission with effect of heart attack in United Kingdom with advanced mathematical tools. Mathematical model is converted into fractional order with the help of fractal fractional operator (FFO). The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the SC-2 system is verified and test the proposed system with flip bifurcation. Also system is investigated for global stability using Lyponove first and second derivative functions. The existence, boundedness, and positivity of the SC-2 is checked which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects of heart attack in united kingdom. Solutions for fractional order system are derived with the help of advanced tool FFO for different fractional values to verify the combine effect of COVID-19 and heart patients. Simulation are carried out to see symptomatic as well as a symptomatic effects of SC-2 in the United Kingdom as well as its global effects, also show the actual behavior of SC-2 which will be helpful to understand the outbreak of SC-2 for heart attack patients and to see its real behavior globally as well as helpful for future prediction and control strategies., (© 2024 Wiley‐VCH GmbH.)

Motile bacteria in hybrid nanofluids cause bioconvection. Bacillus cereus, Pseudomonas viscosa, Bacillus brevis, Salmonella typhimurium, and Pseudomonas fluorescens were used to evaluate their effect and dispersion in the hybrid nanofluid. Using similarity analysis, a two-phase model for mixed bioconvection magnetohydrodynamic flow was developed using hybrid nanoparticles of Al 2 O 3 and Cu (Cu-Al 2 O 3 /water). The parametric investigation, covering the magnetic parameter, permeability coefficient, nanoparticle shape factor, temperature ratio, radiation parameter, nanoparticle fraction ratio, Brownian parameter, thermophoresis parameter, motile bacteria diffusivity, chemotaxis parameter, and Nusselt, Reynold, Prandtl, Sherwood numbers, as well as the number of motile microorganisms', showed significant outcomes. Velocity and shear stresses are sensitive to M, Pr, and [Formula: see text]. Magnetic, radiation, and chemotaxis factors impact bacterial density. The hybrid nanofluid velocity decreases when the magnetic parameter, M, Prandtl number Pr increases, while it increases with the increasing of porosity coefficient, [Formula: see text], and the hybrid nanoparticle ratio N f . The temperature distribution decreases with the increasing of Prandtl number and N f . Increasing temperature differential and bacterium diffusivity increases bacterial aggregation., (© 2024. The Author(s), under exclusive licence to Springer Nature B.V.)

We present a new mathematical model to analyze the dynamics of the Zika virus (ZV) disease with the mutant under the real confirmed cases in Colombia. We give the formulation of the model initially in integer order derivative and then extend it to a fractional order system in the sense of the Mittag-Leffler kernel. We study the properties of the model in the Mittag-Leffler kernel and establish the result. The basic reproduction of the fractional system is computed. The equilibrium points of the Zika virus model are obtained and found that the endemic equilibria exist when the threshold is greater than unity. Further, we show that the model does not possess the backward bifurcation phenomenon. The numerical procedure to solve the problem using the Atangana-Baleanu derivative is shown using the newly established numerical scheme. We consider the real cases of the Zika virus in Colombia outbreak are considered and simulate the model using the nonlinear least square curve fit and computed the basic reproduction number R 0 = 0.4942 , whereas in previous work (Alzahrani et al., 2021) [1], the authors computed the basic reproduction number R 0 = 0.5447 . This is due to the fact that our work in the present paper provides better fitting to the data when using the fractional order model, and indeed the result regarding the data fitting using the fractional model is better than integer order model. We give a sensitivity analysis of the parameters involved in the basic reproduction number and show them graphically. The results obtained through the present numerical method converge to its equilibrium for the fractional order, indicating the proposed scheme's reliability., Competing Interests: The authors declare that they have no conflict of interest., (© 2023 The Authors.)

In this paper, the mathematical modeling of the novel corona virus (COVID-19) is considered. A brief relationship between the unknown hosts and bats is described. Then the interaction among the seafood market and peoples is studied. After that, the proposed model is reduced by assuming that the seafood market has an adequate source of infection that is capable of spreading infection among the people. The reproductive number is calculated and it is proved that the proposed model is locally asymptotically stable when the reproductive number is less than unity. Then, the stability results of the endemic equilibria are also discussed. To understand the complex dynamical behavior, fractal-fractional derivative is used. Therefore, the proposed model is then converted to fractal-fractional order model in Atangana-Baleanu (AB) derivative and solved numerically by using two different techniques. For numerical simulation Adam-Bash Forth method based on piece-wise Lagrangian interpolation is used. The infection cases for Jan-21, 2020, till Jan-28, 2020 are considered. Then graphical consequences are compared with real reported data of Wuhan city to demonstrate the efficiency of the method proposed by us.

Traditional medicines against COVID-19 have taken important outbreaks evidenced by multiple cases, controlled clinical research, and randomized clinical trials. Furthermore, the design and chemical synthesis of protease inhibitors, one of the latest therapeutic approaches for virus infection, is to search for enzyme inhibitors in herbal compounds to achieve a minimal amount of side-effect medications. Hence, the present study aimed to screen some naturally derived biomolecules with anti-microbial properties (anti-HIV, antimalarial, and anti-SARS) against COVID-19 by targeting coronavirus main protease via molecular docking and simulations. Docking was performed using SwissDock and Autodock4, while molecular dynamics simulations were performed by the GROMACS-2019 version. The results showed that Oleuropein, Ganoderic acid A, and conocurvone exhibit inhibitory actions against the new COVID-19 proteases. These molecules may disrupt the infection process since they were demonstrated to bind at the coronavirus major protease's active site, affording them potential leads for further research against COVID-19., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 Elsevier Ltd. All rights reserved.)

A brain tumor is a dynamic system in which cells develop rapidly and abnormally, as is the case with most cancers. Cancer develops in the brain or inside the skull when aberrant and odd cells proliferate in the brain. By depriving the healthy cells of leisure, nutrition, and oxygen, these aberrant cells eventually cause the healthy cells to perish. This article investigated the development of glioma cells in treating brain tumors. Mathematically, reaction-diffusion models have been developed for brain glioma growth to quantify the diffusion and proliferation of the tumor cells within brain tissues. This study presents the formulation the two-stage successive over-relaxation (TSSOR) algorithm based on the finite difference approximation for solving the treated brain glioma model to predict glioma cells in treating the brain tumor. Also, the performance of TSSOR method is compared to the Gauss-Seidel (GS) and two-stage Gauss-Seidel (TSGS) methods in terms of the number of iterations, the amount of time it takes to process the data, and the rate at which glioma cells grow the fastest. The implementation of the TSSOR, TSGS, and GS methods predicts the growth of tumor cells under the treatment protocol. The results show that the number of glioma cells decreased initially and then increased gradually by the next day. The computational complexity analysis is also used and concludes that the TSSOR method is faster compared to the TSGS and GS methods. According to the results of the treated glioma development model, the TSSOR approach reduced the number of iterations by between 8.0 and 71.95%. In terms of computational time, the TSSOR approach is around 1.18-76.34% faster than the TSGS and GS methods., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

The current study deals with the stochastic reaction-diffusion epidemic model numerically with two proposed schemes. Such models have many applications in the disease dynamics of wildlife, human life, and others. During the last decade, it is observed that the epidemic models cannot predict the accurate behavior of infectious diseases. The empirical data gained about the spread of the disease shows non-deterministic behavior. It is a strong challenge for researchers to consider stochastic epidemic models. The effect of the stochastic process is analyzed. So, the SIR epidemic model is considered under the influence of the stochastic process. The time noise term is taken as the stochastic source. The coefficient of the stochastic term is a Borel function, and it is used to control the random behavior in the solutions. The proposed stochastic backward Euler scheme and the proposed stochastic implicit finite difference scheme (IFDS) are used for the numerical solution of the underlying model. Both schemes are consistent in the mean square sense. The stability of the schemes is proven with Von-Neumann criteria and schemes are unconditionally stable. The proposed stochastic backward Euler scheme converges toward a disease-free equilibrium and does not converge toward an endemic equilibrium but also possesses negative behavior. The proposed stochastic IFD scheme converges toward disease-free equilibrium and endemic equilibrium. This scheme also preserves positivity. The graphical behavior of the stochastic SIR model is much similar to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The efficacy of the proposed scheme is shown in the graphical behavior of the test problem for the various values of the parameters., Competing Interests: Competing interestsThe authors declare no competing interest., (© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.)

A topological index is a numerical parameter that is derived mathematically from a graph structure. In chemical graph theory, these indices are used to quantify the chemical properties of chemical compounds. We compute the first and second temperature, hyper temperature indices, the sum connectivity temperature index, the product connectivity temperature index, the reciprocal product connectivity temperature index and the F temperature index of a molecular graph silicate network and silicate chain network. Furthermore, a QSPR study of the key topological indices is provided, and it is demonstrated that these topological indices are substantially linked with the physicochemical features of COVID-19 medicines. This theoretical method to find the temperature indices may help chemists and others in the pharmaceutical industry forecast the properties of silicate networks and silicate chain networks before trying., Competing Interests: The authors declare no conflicts of interest.

In recent years, there are many new definitions that were proposed related to fractional derivatives, and with the help of these definitions, mathematical models were established to overcome the various real-life problems. The true purpose of the current work is to develop and analyze Atangana-Baleanu (AB) with Mittag-Leffler kernel and Atangana-Toufik method (ATM) of fractional derivative model for the Smoking epidemic. Qualitative analysis has been made to `verify the steady state. Stability analysis has been made using self-mapping and Banach space as well as fractional system is analyzed locally and globally by using first derivative of Lyapunov. Also derive a unique solution for fractional-order model which is a new approach for such type of biological models. A few numerical simulations are done by using the given method of fractional order to explain and support the theoretical results., Competing Interests: The authors state that there is no conflict of interest., (Copyright © 2022 Aqeel Ahmad et al.)

We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study., Competing Interests: Competing interestsThe authors declare that they have no competing interests., (© The Author(s) 2022.)

Background: Antiarrhythmic drugs remain the first-line therapy for treatment of idiopathic ventricular arrhythmias., Study Question: The aim of this study was to assess the therapeutic efficacy of extended-release metoprolol succinate (MetS) and carvedilol for idiopathic, frequent, monomorphic premature ventricular contractions (PVCs)., Study Design: Study population consisted of 114 consecutive patients: 71 received MetS and 43 received carvedilol., Measures and Outcomes: All patients underwent 24-hour Holter monitoring at baseline and during drug therapy. PVC-burden response to drug therapy was categorized as "good" (≥80% reduction), "poor" (either <80% reduction or ≤50% increase), and "proarrhythmic" responses (>50% increase) based on change in PVC burden compared with baseline., Results: Most common presenting symptom was palpitations (65.8%), followed by coincidental discovery (29%). The mean MetS and carvedilol dosages were 65.57 ± 30.67 mg/d and 23.66 ± 4.26 mg/d, respectively. "Good," "poor," and "proarrhythmic" responses were observed in 11.3% and 16.3%, 63.4% and 67.4%, and 25.3% and 16.3% of patients treated with MetS and carvedilol, respectively. In patients with relatively high (≥16%) PVC burden, the sum of "poor"/"proarrhythmic" response was observed in 95.5% and 86.4% of patients treated with MetS and carvedilol, respectively. "Proarrhythmic" response was observed in 21.9% of the patients, particularly in the presence of relatively lower (≤10%) baseline PVC burden. Patients with "good" response during beta-blocker therapy had higher baseline daily average intrinsic total heart beats compared with patients with "poor"/"proarrhythmic" response combined (96,437 ± 26,488 vs. 86,635 ± 15,028, P = 0.047, respectively). Side effects and intolerance were observed in 5.6% and 18.6% of patients treated with MetS and carvedilol, respectively., Conclusions: MetS and carvedilol for idiopathic, frequent, monomorphic PVCs are frequently inefficient. Therapeutic efficacy decreases further in patients with relatively high (≥16%) PVC burden. Relatively higher baseline daily intrinsic total heart beats may be used to predict "good" response before beta-blocker therapy., Competing Interests: The authors have no conflicts of interest to declare., (Copyright © 2021 Wolters Kluwer Health, Inc. All rights reserved.)

The current work is of interest to introduce a detailed analysis of the novel fractional COVID-19 model. Non-local fractional operators are one of the most efficient tools in order to understand the dynamics of the disease spread. For this purpose, we intend as an attempt at investigating the fractional COVID-19 model through Caputo operator with order χ ∈ ( 0 , 1 ) . Employing the fixed point theorem, it is shown that the solutions of the proposed fractional model are determined to satisfy the existence and uniqueness conditions under the Caputo derivative. On the other hand, its iterative solutions are indicated by making use of the Laplace transform of the Caputo fractional operator. Also, we establish the stability criteria for the fractional COVID-19 model via the fixed point theorem. The invariant region in which all solutions of the fractional model under investigation are positive is determined as the non-negative hyperoctant R + 7 . Moreover, we perform the parameter estimation of the COVID-19 model by utilizing the non-linear least squares curve fitting method. The sensitivity analysis of the basic reproduction number R 0 c is carried out to determine the effects of the proposed fractional model's parameters on the spread of the disease. Numerical simulations show that all results are in good agreement with real data and all theoretical calculations about the disease., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2021 The Author(s).)

The article deals with the analysis of the fractional COVID-19 epidemic model (FCEM) with a convex incidence rate. Keeping in view the fading memory and crossover behavior found in many biological phenomena, we study the coronavirus disease by using the noninteger Caputo derivative (CD). Under the Caputo operator (CO), existence and uniqueness for the solutions of the FCEM have been analyzed using fixed point theorems. We study all the basic properties and results including local and global stability. We show the global stability of disease-free equilibrium using the method of Castillo-Chavez, while for disease endemic, we use the method of geometrical approach. Sensitivity analysis is carried out to highlight the most sensitive parameters corresponding to basic reproduction number. Simulations are performed via first-order convergent numerical technique to determine how changes in parameters affect the dynamical behavior of the system., (© 2021 John Wiley & Sons, Ltd.)

Two efficient integration schemes, new extended hyperbolic function and generalized tanh are employed to discover optical soliton solutions to magneto-optic waveguides that retains anti-cubic form of nonlinear refractive index. Bright, dark, periodic singular, singular, and combo soliton solutions have created. These solutions expose the comprehensive variety of soliton solutions., (© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.)

This study provides a detailed exposition of in-hospital community-acquired methicillin-resistant S. aureus (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant S. aureus (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative. We show the existence and uniqueness of the solutions of the fractional staph infection model through fixed-point theorems. Moreover, stability analysis and iterative solutions are furnished by the recursive procedure. We make use of the parameter values obtained from the Beth Israel Deaconess Medical Center. Analysis of the model under investigation shows that the disease-free equilibrium existing for all parameters is globally asymptotically stable when both R 0 H and R 0 C are less than one. We also carry out the sensitivity analysis to identify the most sensitive parameters for controlling the spread of the infection. Additionally, the solution for the above-mentioned model is obtained by the Laplace-Adomian decomposition method and various simulations are performed by using convenient fractional-order α ., (© Korean Society for Informatics and Computational Applied Mathematics 2021.)

We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated M -derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations., Competing Interests: Competing interestsThe authors declare that they have no competing interests., (© The Author(s) 2021.)

This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized, and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo's sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17., (© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021.)

This paper describes the existence and stability of the hepatitis B epidemic model with a fractional-order derivative in Atangana-Baleanu sense. Some new results are handled by using the Sumudu transform. The existence and uniqueness of the equilibrium solution are presented using the Banach fixed-point theorem. Moreover, sensitivity analysis complemented by simulations is performed to determine how changes in parameters affect the dynamical behavior of the system. The numerical simulations are carried out using a predictor-corrector scheme to demonstrate the obtained results.

We consider an epidemic disease system by an additive fractional white noise to show that epidemic diseases may be more competently modeled in the fractional-stochastic settings than the ones modeled by deterministic differential equations. We generate a new SIRS model and perturb it to the fractional-stochastic systems. We study chaotic behavior at disease-free and endemic steady-state points on these systems. We also numerically solve the fractional-stochastic systems by an trapezoidal rule and an Euler type numerical method. We also associate the SIRS model with fractional Brownian motion by Wick product and determine numerical and explicit solutions of the resulting system. There is no SIRS-type model which considers fractional epidemic disease models with fractional white noise or Wick product settings which makes the paper totally a new contribution to the related science., Competing Interests: The authors declare that there is no conflict of interests regarding the publication of this paper., (© 2020 Elsevier Ltd. All rights reserved.)

In this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo with the fractional parameter χ, where 0<χ≤1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top. The non-integer-order model suggested in the present study depicts the past behavior of the concentration of the solution on the basis of having information of the initial concentration present in the dye. Being nonlinear, it carries the possibility to have no exact solution. However, the Lipchitz condition shows the existence and uniqueness of the underlying model's solution in non-integer-order settings. From a numerical simulation viewpoint, three numerical techniques having first order convergence have been employed to illustrate the numerical results obtained.

We discussed anthroponotic cutaneous leishmania transmission in this article, due to its large effect on the community in the recent years. The mathematical model is developed for anthroponotic cutaneous leishmania transmission, and its qualitative behavior is taken under consideration. The threshold number R 0 of the model is derived using the next-generation method. In the disease-free case, local and global stability is carried out with the condition that R 0 will be less than one. The global stability at the disease-free equilibrium point has been derived by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, the local and global stability holds with some conditions, and R 0 is greater than unity. The global stability at the endemic equilibrium point is established with the help of a geometrical approach which is the generalization of Lyapunov theory, by using the third additive compound matrix. The sensitivity analysis of the threshold number with other parameters is also taken into account. Several graphs of important parameters are discussed in the last section., (© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020.)

In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations.

In the present study, the fractional version with respect to the Atangana-Baleanu fractional derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu fractional derivative operator in the caputo sense. To believe upon the results obtained, the fractional order α has been allowed to vary between ( 0 , 1 ] , whereupon the physical observations match with those obtained in the classical case, but the fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of fractional order derivatives for ABC. Finally, the fractional forward Euler method in the classical caputo sense has been used to illustrate the better performance of the numerical method obtained via the Atangana-Baleanu fractional derivative operator in the caputo sense.

Methods for isolation and quantification of circulating tumor cells (CTCs) are attracting more attention every day, as the data for their unprecedented clinical utility continue to grow. However, the challenge is that CTCs are extremely rare (as low as 1 in a billion of blood cells) and a highly sensitive and specific technology is required to isolate CTCs from blood cells. Methods utilizing microfluidic systems for immunoaffinity-based CTC capture are preferred, especially when purity is the prime requirement. However, antibody immobilization strategy significantly affects the efficiency of such systems. In this study, two covalent and two bioaffinity antibody immobilization methods were assessed with respect to their CTC capture efficiency and selectivity, using an anti-epithelial cell adhesion molecule (EpCAM) as the capture antibody. Surface functionalization was realized on plain SiO 2 surfaces, as well as in microfluidic channels. Surfaces functionalized with different antibody immobilization methods are physically and chemically characterized at each step of functionalization. MCF-7 breast cancer and CCRF-CEM acute lymphoblastic leukemia cell lines were used as EpCAM positive and negative cell models, respectively, to assess CTC capture efficiency and selectivity. Comparisons reveal that bioaffinity based antibody immobilization involving streptavidin attachment with glutaraldehyde linker gave the highest cell capture efficiency. On the other hand, a covalent antibody immobilization method involving direct antibody binding by N-(3-dimethylaminopropyl)-N'-ethylcarbodiimide hydrochloride (EDC)-N-hydroxysuccinimide (NHS) reaction was found to be more time and cost efficient with a similar cell capture efficiency. All methods provided very high selectivity for CTCs with EpCAM expression. It was also demonstrated that antibody immobilization via EDC-NHS reaction in a microfluidic channel leads to high capture efficiency and selectivity.

Objective: To measure the Tp-e value, which shows the spatial distribution of cardiac repolarization and is defined as a possible predictor for ventricular arrhythmia among patients with aortic sclerosis (AS), and to compare this parameter's length to QTc length within the same population., Method: 60 patients that have been diagnosed with AS have been prospectively included in this study., Results: 60 AS and 64 control patients were evaluated as part of the study. The median age, prevalence for hypertension and diabetes, baseline medications and laboratory results of the groups were similar. The Electrocardiographic QT length of both groups were found similar. In the AS group Tp-e tangent and Tp-e tail values were more longer than control group (P < 0.001). Tp-e tangent index and Tp-e tail index values were also statistically higher among AS patients when compared to the control group. (P < 0.001)., Conclusion: Our study showed that Tp-e durations had increased in AS patients with no structural coronary heart disease. AS causes local degeneration on the aortic root and also has a negative effect on the total cardiac spatial repolarization.