Matematik Bölümü

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A 6-Point Subdivision Scheme and Its Applications for the Solution of 2nd Order Nonlinear Singularly Perturbed Boundary Value Problems
(Amer inst Mathematical Sciences-aims, 2020) Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; Mustafa, Ghulam
In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
Citation - WoS: 35
Adaptive Fractional-Order Blood Glucose Regulator Based on High-Order Sliding Mode Observer
(inst Engineering Technology-iet, 2019) Heydarinejad, Hamid; Baleanu, Dumitru; Delavari, Hadi
Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.
Citation - WoS: 18
Citation - Scopus: 24
Analysis for Fractional-Order Predator-Prey Model With Uncertainty
(inst Engineering Technology-iet, 2019) Baleanu, Dumitru; Thangapandi, Kalidas; Perera, Shyam Sanjeewa Nishantha; Narayanamoorthy, Samayan
Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.
Citation - WoS: 69
Citation - Scopus: 90
Analysis of Fractional Model of Guava for Biological Pest Control With Memory Effect
(Elsevier, 2021) Ganbari, Behzad; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
Introduction: Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives: The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods: Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results: The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion: The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - Scopus: 1
Analytical Results for Positivity of Discrete Fractional Operators With Approximation of the Domain of Solutions
(Amer inst Mathematical Sciences-aims, 2022) O'Regan, Donal; Baleanu, Dumitru; Hamed, Y. S.; Elattar, Ehab E.; Mohammed, Pshtiwan Othman
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 0 and epsilon > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of epsilon and theta.
Citation - WoS: 391
Citation - Scopus: 431
Anomalous Diffusion Expressed Through Fractional Order Differential Operators in the Bloch-Torrey Equation
(Academic Press inc Elsevier Science, 2008) Abdullah, Osama; Baleanu, Dumitru; Zhou, Xiaohong Joe; Magin, Richard L.
Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on d iffusi on -weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (turn (2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology. (c) 2007 Elsevier Inc. All rights reserved.
Citation - WoS: 72
Citation - Scopus: 81
An Application of Derivative and Continuous Wavelet Transforms To the Overlapping Ratio Spectra for the Quantitative Multiresolution of a Ternary Mixture of Paracetamol, Acetylsalicylic Acid and Caffeine in Tablets
(Elsevier Science Bv, 2005) Özdemir, A; Baleanu, D; Dinç, E
Quantitative multi resolution of tablets and ternary mixtures of paracetamol (PAR), acetylsalicylic acid (ASP) and caffeine (CAF) having strongly overlapping spectra was accomplished by two graphical transform methods as ratio spectra first derivative-zero crossing and ratio spectra-continuous wavelet transform-zero crossing (ratio spectra CWT-zero crossing) methods. In this study, ratio spectra derivative-zero crossing and ratio spectra CWT-zero crossing methods are based on the use of transformed signals of the ratio spectra and their calibration graphs were obtained by measuring the dA/dlambda and CWT amplitudes of the ratio spectra corresponding to zero crossing points. For the comparison purpose. PLS calibration method was applied to predict the content of the same mixtures containing the subject active Compounds. The obtained calibrations were tested by using the synthetic mixtures and standard addition technique and they applied to the simultaneous determination of PAR, ASP and CAF in commercial pharmaceutical preparation. The obtained results were statistically compared with each other as well as those obtained by HPLC method and they showed good agreement. (C) 2004 Published by Elsevier B.V.
Citation - WoS: 26
Citation - Scopus: 31
Asymptotic Solutions of Fractional Interval Differential Equations With Nonsingular Kernel Derivative
(Amer inst Physics, 2019) Ahmadian, A.; Salimi, M.; Ferrara, M.; Baleanu, D.; Salahshour, S.
Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters. Published under license by AIP Publishing.
Citation - WoS: 20
Citation - Scopus: 20
Bipolar Intuitionistic Fuzzy Graph Based Decision-Making Model To Identify Flood Vulnerable Region
(Springer Heidelberg, 2023) Augustin, Felix; Narayanamoorthy, Samayan; Ahmadian, Ali; Balaenu, Dumitru; Kang, Daekook; Nithyanandham, Deva
Bipolar intuitionistic fuzzy graphs (BIFG) are an extension of fuzzy graphs that can effectively capture uncertain or imprecise information in various applications. In graph theory, the covering, matching, and domination problems are benchmark concepts applied to various domains. These concepts may not be defined precisely using a crisp graph when the vertices and edges are more uncertain. Therefore, this study defines the covering, matching and domination concepts in bipolar intuitionistic fuzzy graphs (BIFG) using effective edges with certain important results. To define these concepts when the effective edges are absent, some novel approaches are discussed. To illustrate the domination concepts, the applications in disaster management and location selection problems are discussed. Further, a BIFG-based decision-making model is designed to identify the flood-vulnerable zones in Chennai, where the city's most and least vulnerable zones are identified. From the proposed model, Kodambakkam (Z(10)) is the most susceptible zone in Chennai. Finally, a comparative analysis is done with the existing techniques to show the efficiency of the model.
Citation - WoS: 28
Citation - Scopus: 32
Boger Nanofluid: Significance of Coriolis and Lorentz Forces on Dynamics of Rotating Fluid Subject To Suction/Injection Via Finite Element Simulation
(Nature Portfolio, 2022) Siddique, Imran; Hussain, Sajjad; Ali, Liaqat; Baleanu, Dumitru; Ali, Bagh
This study briefings the roles of Coriolis, and Lorentz forces on the dynamics of rotating nanofluids flow toward a continuously stretching sheet. The nanoparticles are incorporated because of their unusual qualities like upgrade the thermal transportation, which are very important in heat exchangers, modern nanotechnology, electronics, and material sciences. The primary goal of this study is to improve heat transportation. Appropriate similarity transformations are applied for the principal PDEs to transform into nonlinear dimensionless PDEs. A widely recognized Numerical scheme known as the Finite Element Method is employed to solve the resultant convective boundary layer balances. Higher input in the solvent fraction parameter has a rising effect on the primary velocity and secondary velocity magnitude, and decreasing impact on the distributions of temperature. It is seen that growing contributions of the Coriolis, and Lorentz forces cause to moderate the primary and secondary velocities, but the temperature and concentration functions show opposite trend. The concentration, temperature, and velocities distributions for suction case is prominently than that of injection case, but inverse trend is observed for local Nusselt and Sherwood numbers. These examinations are relevant to the field of plastic films, crystal growing, paper production, heat exchanger, and bio-medicine.
Citation - WoS: 31
Citation - Scopus: 43
Caputo Sir Model for Covid-19 Under Optimized Fractional Order
(Springer, 2021) Ullah, Malik Z.; Baleanu, Dumitru; Alshomrani, Ali S.
Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case (nu=1). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.
Citation - WoS: 8
Citation - Scopus: 9
Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
(Hindawi Ltd, 2013) Agarwal, P.; Purohit, S. D.; Baleanu, D.
We apply generalized operators of fractional integration involving Appell's function F-3(.) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdelyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
Citation - WoS: 39
Citation - Scopus: 48
Chaotic Attractors With Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors
(Mdpi, 2018) Baleanu, Dumitru; Tchier, Fairouz; Solis Perez, Jesus Emmanuel; Francisco Gomez-Aguilar, Jose
This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and beta-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and beta-conformable attractors are provided to illustrate the effectiveness of the proposed method.
Citation - WoS: 31
Citation - Scopus: 40
Chemometric Determination of Naproxen Sodium and Pseudoephedrine Hydrochloride in Tablets by Hplc
(Pharmaceutical Soc Japan, 2006) Özdemir, A; Aksoy, H; Üstündag, Ö; Baleanu, D; Dinç, E
A new chemometric determination by high-performance liquid chromatography (HPLC) with photodiode array (PDA) detection was implemented for the simultaneous determination of naproxen sodium and pseudoephedrine hydrochloride in tablets. Three chemometric calibration techniques, classical least squares (CLS), principle component regression (PCR) and partial least squares (PLS) were applied to the peak area at multiwavelength PDA detector responses. The combinations of HPLC with chernometric calibration techniques were called HPLC-CLS, HPLC-PCR and HPLC-PLS. For comparison purposes the HPLC method called the classic HPLC method was used to confirm the results obtained from combined HPLC-chemometric calibration techniques. A good chromatographic separation between two drugs with losartan potassium as an internal standard was achieved using a Waters Symmetry (R) C18 Column 5 mu m 4.6 +/- 250 mm and a mobile phase containing 0.2 m acetate buffer and acetonitrile (v/v, 40 : 60). The multiwavelength PDA detection was measured at five different wavelengths. The chromatograms were recorded as a training set in the mobile phase. Three HPLC-chemometric calibrations and the classic-HPLC method were used to test the synthetic mixtures of naproxen sodium and pseudoephedrine hydrochloride in the presence of the internal standard. The HPLC-chemometric approaches were applied to real samples containing drugs of interest. The experimental results obtained from HPLC-chemometric calibrations were compared with those obtained by a classic HPLC method.
Citation - WoS: 16
Citation - Scopus: 16
Comparative Application of Wavelet Approaches To Absorption and Ratio Spectra for the Simultaneous Determination of Diminazene Aceturate and Phenazone in Veterinary Granules for Injection
(Govi-verlag Pharmazeutischer verlag Gmbh, 2005) Dinç, E; Baleanu, Dumitru; Kanbur, M; Baleanu, D; Matematik
A comparison of two wavelet approaches, Daubechies and reverse Biorthogonal, is described for the quantitative resolution of a binary mixture of diminazene aceturate (DIMA) and phenazone (PHE) in veterinary granules for injection without any chemical separation. These two approaches were specified as db4 (a = 180) and rbior3.7 (a = 125) respectively, after testing the signal analysis parameters for the overlapping absorption spectra and ratio spectra. In the first step db4 (a = 180) was applied to the original absorbance data vector of DIMA and PHE. In the second step rbio3.7 (a = 125) was applied to the ratio spectra data vectors of DIMA using the divisor PHE. The same approach was also subjected to the ratio spectra of PHE using the divisor DIMA. The db4 (a = 180) and rbior3.7 (a = 125) calibration graphs were constructed using the transformation values obtained in the wavelet domain. In the method validation, the wavelet calibration functions were tested using synthetic mixtures and the standard addition technique. The simultaneous quantitative analysis of DIMA and PHE in the commercial veterinary preparation was achieved by the elaborated methods. The assay results were compared with each other and good agreement was observed.
Citation - WoS: 24
Citation - Scopus: 26
Comparative Spectral Analysis of Veterinary Powder Product by Continuous Wavelet and Derivative Transforms
(Pergamon-elsevier Science Ltd, 2007) Kanbur, Murat; Baleanu, Dumitru; Dinc, Erdal
Comparative simultaneous determination of chlortetracycline and benzocaine in the commercial veterinary powder product was carried out by continuous wavelet transform (CWT) and classical derivative transform (or classical derivative spectrophotometry). In this quantitative spectral analysis, two proposed analytical methods do not require any chemical separation process. In the first step, several wavelet families were tested to find an optimal CWT for the overlapping signal processing of the analyzed compounds. Subsequently, we observed that the coiflets (COIF-CWT) method with dilation parameter, a = 400, gives suitable results for this analytical application. For a comparison, the classical derivative spectrophotometry (CDS) approach was also applied to the simultaneous quantitative resolution of the same analytical problem. Calibration functions were obtained by measuring the transform amplitudes corresponding to zero-crossing points for both CWT and CDS methods. The utility of these two analytical approaches were verified by analyzing various synthetic mixtures consisting of chlortetracycline and benzocaine and they were applied to the real samples consisting of veterinary powder formulation. The experimental results obtained from the COIF-CWT approach were statistically compared with those obtained by classical derivative spectrophotometry and successful results were reported. (C) 2006 Elsevier B.V. All rights reserved.
Citation - WoS: 64
Citation - Scopus: 63
Comparative Study of Artificial Neural Network Versus Parametric Method in Covid-19 Data Analysis
(Elsevier, 2022) Colak, Andac Batur; Sindhu, Tabassum Naz; Lone, Showkat Ahmad; Alsubie, Abdelaziz; Jarad, Fahd; Shafiq, Anum
Since the previous two years, a new coronavirus (COVID-19) has found a major global problem. The speedy pathogen over the globe was followed by a shockingly large number of afflicted people and a gradual increase in the number of deaths. If the survival analysis of active individuals can be predicted, it will help to contain the epidemic significantly in any area. In medical diagnosis, prognosis and survival analysis, neural networks have been found to be as successful as general nonlinear models. In this study, a real application has been developed for estimating the COVID-19 mortality rates in Italy by using two different methods, artificial neural network modeling and maximum likelihood estimation. The predictions obtained from the multilayer artificial neural network model developed with 9 neurons in the hidden layer were compared with the numerical results. The maximum deviation calculated for the artificial neural network model was -0.14% and the R value was 0.99836. The study findings confirmed that the two different statistical models that were developed had high reliability.
Citation - WoS: 51
Citation - Scopus: 56
Comparative Study of the Continuous Wavelet Transform, Derivative and Partial Least Squares Methods Applied To the Overlapping Spectra for the Simultaneous Quantitative Resolution of Ascorbic Acid and Acetylsalicylic Acid in Effervescent Tablets
(Elsevier Science Bv, 2005) Ozdemir, A; Baleanu, D; Dinç, E
The simultaneous spectrophotometric determination of ascorbic acid (AA) and acetylsalicylic acid (ASA) in effervescent tablets in the presence of the overlapping spectra was accomplished by the continuous wavelet transform (CWT), derivative spectrophotometry (DS) and partial least squares (PLS) approaches without using any chemical pre-treatment. CWT and DS calibration equations for AA and ASA were obtained by measuring the CWT and DS amplitudes corresponding to zero-crossing points of spectra obtained by plotting continuous wavelet coefficients and first-derivative absorbance values versus the wavelengths, respectively. The PLS calibration was constructed by using the concentration set and its full absorbance data consisting of 850 points from 220 to 305 urn in the range of 210-310 nun. These three methods were tested by analyzing the synthetic mixtures of the above drugs and they were applied to the real samples containing two commercial pharmaceutical preparations of subjected drugs. A comparative study was carried out by using the experimental results obtained from three analytical methodologies and precise and accurate results were obtained. (c) 2004 Published by Elsevier B.V.
Citation - WoS: 31
Citation - Scopus: 32
A Comparative Study on Biodegradation and Mechanical Properties of Pressureless Infiltrated Ti/Ti6al4v-mg Composites
(Elsevier Science Bv, 2016) Karakas, M. Serdar; Esen, Ziya; Butev, Ezgi
The mechanical response and biodegradation behavior of pressureless Mg-infiltrated Ti-Mg and Ti6Al4V-Mg composites were investigated by compression and simulated body fluid immersion tests, respectively. Prior porous preforms were surrounded uniformly with magnesium as a result of infiltration and the resultant composites were free of secondary phases and intermetallics. Although the composites' compressive strengths were superior compared to bone, both displayed elastic moduli similar to that of cortical bone and had higher ductility with respect to their starting porous forms. However, Ti-Mg composites were unable to preserve their mechanical stabilities during in-vitro tests such that they fractured in multiple locations within 15 days of immersion. The pressure generated by H-2 due to rapid corrosion of magnesium caused failure of the Ti-Mg composites through sintering necks. On the other hand, the galvanic effect seen in Ti6Al4V-Mg was less severe compared to that of Ti-Mg. The degradation rate of magnesium in Ti6Al4V-Mg was slower, and the composites were observed to be mechanically stable and preserved their integrities over the entire 25-day immersion test. Both composites showed bioinert and biodegradable characteristics during immersion tests and magnesium preferentially corroded leaving porosity behind while Ti/Ti6Al4V remained as a permanent scaffold. The porosity created by degradation of magnesium was refilled by new globular agglomerates. Mg(OH)(2) and CaHPO4 phases were encountered during immersion tests while MgCl2 was detected during only the first 5 days. Both composites were classified as bioactive since the precipitation of CaHPO4 phase is known to be precursor of hydroxyapatite formation, an essential requirement for an artificial material to bond to living bone. (C) 2016 Elsevier Ltd. All rights reserved.
Citation - WoS: 17
Citation - Scopus: 19
Competitive Analysis for Stochastic Influenza Model With Constant Vaccination Strategy
(inst Engineering Technology-iet, 2019) Raza, Ali; Rafiq, Muhammad; Arif, Muhammad Shoaib; Ali, Muhammad Asghar; Baleanu, Dumitru
This manuscript discusses a competitive analysis of stochastic influenza model with constant vaccination strategy. The stochastic influenza model is comparatively more pragmatic versus the deterministic influenza model. The effect of influenza generation number holds in the stochastic model. If the value of this number is less than one, this situation will help us to control the disease in a population. A greater than one value of this threshold number shows the persistence of disease to become endemic. The proposed structure for the stochastic influenza model as stochastic non-standard finite difference scheme conserve all vital characteristics like positivity, boundedness and dynamical consistency defined by Mickens.

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