Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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COAR Access Rights: search.filters.coarAccessRights.open accessSubject: search.filters.subject.Stability Analysis

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Now showing 1 - 10 of 49
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage
    (Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, Thabet
    Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 20
    On the Decomposition and Analysis of Novel Simultaneous Seiqr Epidemic Model
    (Amer inst Mathematical Sciences-aims, 2023) Palanivelu, Balaganesan; Jayaraj, Renuka; Baleanu, Dumitru; Dhandapani, Prasantha Bharathi; Umapathy, Kalpana
    In this manuscript, we are proposing a new kind of modified Susceptible Exposed Infected Quarantined Recovered model (SEIQR) with some assumed data. The novelty imposed here in the study is that we are studying simultaneously SIR, SEIR, SIQR, and SEQR pandemic models with the same data unchanged as the SEIQR model. We are taking this model a step ahead by using a non-helpful transition because it was mostly skipped in the literature. All sorts of features that are essential to study the models, such as basic reproduction number, stability analysis, and numerical simulations have been examined for this modified model with other models.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 11
    Monkeypox Viral Transmission Dynamics and Fractional-Order Modeling With Vaccination Intervention
    (World Scientific Publ Co Pte Ltd, 2023) Kumar, Sachin; Baleanu, Dumitru; Nisar, Kottakkaran sooppy; Singh, Jaskirat pal
    A current outbreak of the monkeypox viral infection, which started in Nigeria, has spread to other areas of the globe. This affects over 28 nations, including the United Kingdom and the United States. The monkeypox virus causes monkeypox (MPX), which is comparable to smallpox and cowpox (MPXV). The monkeypox virus is a member of the Poxviridae family and belongs to the Orthopoxvirus genus. In this work, a novel fractional model for Monkeypox based on the Caputo derivative is explored. For the model, two equilibria have been established: disease-free and endemic equilibrium. Using the next-generation matrix and Castillo's technique, if R-0 < 1 the global asymptotic stability of disease-free equilibrium is shown. The linearization demonstrated that the endemic equilibrium point is locally asymptotically stable if R-0 > 1. Using the parameter values, the model's fundamental reproduction rates for both humans and non-humans are calculated. The existence and uniqueness of the solution are proved using fixed point theory. The model's numerical simulations demonstrate that the recommended actions will cause the infected people in the human and non-human populations to disappear.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    On a Novel Fuzzy Fractional Retarded Delay Epidemic Model
    (Amer inst Mathematical Sciences-aims, 2022) Thippan, Jayakumar; Baleanu, Dumitru; Sivakumar, Vinoth; Dhandapani, Prasantha Bharathi
    The traditional compartmental epidemic models such as SIR, SIRS, SEW consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the changing rate in every population case is notably negligible, That's why we are preferring to calculate them fractionally using FFDE. Using Lofti's fuzzy concept we are picturing the models after that we are estimating their non-integer values using three distinct methodologies LADM-4, DTM-4 for arbitrary fractional-order alpha(i), and RKM-4. At alpha(i) = 1, comparison of the estimations will be done. In addition to the simulation, works of numerical estimations, the existence of steady states, equilibrium points, and stability analysis are all done.
  • Article
    Citation - WoS: 132
    Citation - Scopus: 158
    On a New and Generalized Fractional Model for a Real Cholera Outbreak
    (Elsevier, 2022) Ghassabzade, Fahimeh Akhavan; Nieto, Juan J.; Jajarmi, Amin; Baleanu, Dumitru
    In this paper, a new mathematical model involving the general form of Caputo fractional derivative is studied for a real case of cholera outbreak. Fundamental properties of the new model including the equilibrium points as well as the basic reproduction number are explored. Also, an efficient approximation scheme on the basis of product-integration rule is established to solve the new model. Several kernel functions for the general fractional derivative are tested, and the results are compared with the real data of a cholera outbreak in Yemen. As a consequence, we find a special case in which the aforesaid outbreak is described better, for the corresponding numerical simulations are closer to the real data than the other classical and fractional frameworks. Next, we apply the most realistic model to investigate the effect of vaccination on the considered cholera outbreak. Simulation results show that earlier vaccination could reduce the number of infected individuals effectively, so mortality would have been reduced considerably if the vaccination had been performed earlier. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
  • Article
    Citation - WoS: 4
    Citation - Scopus: 6
    Numerical Treatments for the Optimal Control of Two Types Variable-Order Covid-19 Model
    (Elsevier, 2022) Al-Mekhlafi, Seham; Shatta, Salma; Baleanu, Dumitru; Sweilam, Nasser
    In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable -order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 7
    New Applications Related To Hepatitis C Model
    (Amer inst Mathematical Sciences-aims, 2022) Raza, Ali; Akgul, Ali; Iqbal, Zafar; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Jarad, Fahd; Ahmed, Nauman
    The main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. It is proved by the standard results that the virus-free equilibrium state is locally asymptotically stable if the value of R-0 is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if R-0 is chosen greater than unity. The Routh-Hurwitz criterion is applied to prove the local stability of the system. Further, the disease-free equilibrium state is globally asymptotically stable if R-0 < 1. The viral disease model is studied after reshaping the integer-order hepatitis C model into the fractal-fractional epidemic illustration. The proposed numerical method attains the fixed points of the model. This fact is described by the simulated graphs. In the end, the conclusion of the manuscript is furnished.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 19
    Construction and Numerical Analysis of a Fuzzy Non-Standard Computational Method for the Solution of an Seiqr Model of Covid-19 Dynamics
    (Amer inst Mathematical Sciences-aims, 2022) Ahmed, Nauman; Rafiq, Muhammad; Akgul, Ali; Raza, Ali; Ahmad, Muhammad Ozair; Jarad, Fahd; Dayan, Fazal
    This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Computational Analysis of Covid-19 Model Outbreak With Singular and Nonlocal Operator
    (Amer inst Mathematical Sciences-aims, 2022) Farman, Muhammad; Akgul, Ali; Partohaghighi, Mohammad; Jarad, Fahd; Amin, Maryam
    The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of R0 and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Computational Algorithms for the Analysis of Cancer Virotherapy Model
    (Tech Science Press, 2022) Baleanu, Dumitru; Rafiq, Muhammad; Abbas, Syed Zaheer; Siddique, Abubakar; Javed, Umer; Nazir, Zaighum; Raza, Ali
    Cancer is a common term for many diseases that can affect any part of the body. In 2020, ten million people will die due to cancer. A worldwide leading cause of death is cancer by the World Health Organization (WHO) report. Interaction of cancer cells, viral therapy, and immune response are identified in this model. Mathematical and computational modeling is an effective tool to predict the dynamics of cancer virotherapy. The cell population is categorized into three parts like uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). The modeling of cancer-like diseases is based on the law of mass action (the rate of change of reacting substances is directly proportional to the product of interacting substances). Positivity, boundedness, equilibria, threshold analysis, are part of deterministic modeling. Later on, a numerical analysis is designed by using the standard and non-standard finite difference methods. The non-standard finite difference method is developed to study the long-term behavior of the cancer model. For its efficiency, a comparison of the methods is investigated.