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Öğe A mathematical analysis and simulation for Zika virus model with time fractional derivative(Wiley, 2020) Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Rizwan, Muhammad; Ahmad, Muhammad OzairZika is a flavivirus that is transmitted to humans either through the bites of infected Aedes mosquitoes or through sexual transmission. Zika has been associated with congenital anomalies, like microcephalus. We developed and analyzed the fractional-order Zika virus model in this paper, considering the vector transmission route with human influence. The model consists of four compartments: susceptible individuals arex(1)(t), infected individuals arex(2)(t),x(3)(t)shows susceptible mosquitos, andx(4)(t)shows the infected mosquitos. The fractional parameter is used to develop the system of complex nonlinear differential equations by using Caputo and Atangana-Baleanu derivative. The stability analysis as well as qualitative analysis of the fractional-order model has been made and verify the non-negative unique solution. Finally, numerical simulations of the model with Caputo and Atangana Baleanu are discussed to present the graphical results for different fractional-order values as well as for the classical model. A comparison has been made to check the accuracy and effectiveness of the developed technique for our obtained results. This investigative research leads to the latest information sector included in the evolution of the Zika virus with the application of fractional analysis in population dynamics.Öğe Analysis and Modelling of HIV/AIDS Model with Fractional Order Parameter Estimation(Natural Sciences Publishing, 2022) Farman, Muhammad; Raza, Ali; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Iqbal, Muhammad SajidIn this paper, nonlinear fractional order HIV/AIDS mathematical model is discussed epidemic problems for the complex transmission of the disease. It is accepted that susceptible wind up contaminated by means of sexual contacts with infective eventually create AIDS. The point of this task was to amend transmission models recently created to represent HIV transmission and AIDS related mortality. The Caputo-Fabrizio fractional derivative operator of order ? ? (0,1) is used to obtain fractional differential equations structure. The stability fractional order model was developed and the unique non-negative solution was tested. The numerical simulations are performed using an iterative technique. Some new results are being viewed with the help of Sumudo transform. Nonetheless, according to Banach, the related findings are given nonlinear functional analysis and fixed point theory. However, mathematical simulations are also acknowledged to evaluate the impact of the model’s parameter by decreasing the fractional values and showing the effect of the b fractional parameter on our obtained solutions. The impact of various parameters is represented graphically. © 2022. NSP Natural Sciences Publishing Cor.Öğe Analysis of HIV/AIDS model with Mittag-Leffler kernel(Amer Inst Mathematical Sciences-Aims, 2022) Akram, Muhammad Mannan; Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Partohaghigh, Mohammad; Jarad, FahdRecently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.Öğe Bacillus Calmette Guerin (BCG) Immunotherapy for Bladder Cancer: A Control and Mathematical Analysis(Springer, 2021) Akgül, Ali; Farman, Muhammad; Ahmad, Aqeel; Saleem, Muhammad UmerIn this manuscript, Immunotherapy with Bacillus Calmette Guerin (BCG) vaccine is devised for treating spherical bladder cancer. We considered the cancer model regarding tumor-immune connections in the bladder as a result of BCG therapy and check the input and output of the system. Controllability and observability are treated for the logistic model and exponential model for cancer according to parameter values. Consider the system for stability investigation about the point of equilibrium and taking Bacillus Calmette Guerin (BCG) vaccine concentration as an input and effector cells are output in the system under consideration. The model clarifies that the concentration of immunotherapy should be held in prescribed limits. Also, numerical simulations are carried of the proposed techniques to show the actual behavior of the system to support the biological results. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.Öğe Controllability of PDEs model for type 1 diabetes(Wiley, 2022) Saleem, Muhammad Umer; Aslam, Muhammad; Akgul, Ali; Farman, Muhammad; Bibi, RabiaType 1 diabetes is the worldwide issue nowadays. Partial differential equations (PDEs) models are used to control the disease with different techniques. Efforts are being made to find the controllability of the model for designing the feedback loop control. The concept of controllability and observability is used for the purpose to control the human glucose insulin systems by designing a feedback loop control if the system is controllable and observable. Return method is used to find controllability of the model. This technique is more reliable in case of PDE model to design the fully automatic artificial pancreas to control the diseases.Öğe Dynamical behavior of tumor-immune system with fractal-fractional operator(Amer Inst Mathematical Sciences-Aims, 2022) Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Nisar, Kottakkaran Sooppy; Vijayakumar, VelusamyIn this paper, the dynamical behavior of the fractional-order cancer model has been analyzed with the fractal-fractional operator, which discretized the conformable cancer model. The fractional-order model consists of the system of nonlinear fractional differential equations. Also, we discuss the fractional-order model to check the relationship between the immune system and cancer cells by mixing IL-12 cytokine and anti-PD-L1 inhibitor. The tumor-immune model has been studied qualitatively as well as quantitatively via Atangana-Baleanu fractal-fractional operator. The nonlinear analysis is used to check the Ulam-Hyres stability of the proposed model. Moreover, the dynamical behavior for the fractional-order model has been checked by using a fractal-fractional operator with a generalized Mittag-Leffler Kernel and verifying the effect of fractional parameters. Finally, the obtained solutions are interpreted biologically, and simulations are carried out to illustrate cancer disease and support theoretical results, which will be helpful for further analysis and to control the effect of cancer in the community.Öğe Dynamical behaviour of fractional-order finance system(Indian Acad Sciences, 2020) Farman, Muhammad; Akguel, Ali; Saleem, Muhammad Umer; Imtiaz, Sumaiyah; Ahmad, AqeelIn this paper, we developed the fractional-order finance system transmission model. The main objective of this paper is to construct and evaluate a fractional derivative to track the shape of the dynamic chaotic financial system of fractional order. The numerical solution for fractional-order financial system is determined using the Atangana-Baleanu-Caputo (ABC) and Caputo derivatives. Picard-Lindelof's method shows the existence and uniqueness of the solution. Numerical techniques show that ABC derivative strategy can be used effectively to overcome the risk of investment. An active control strategy for controlling chaos is used in this system. The stabilisation of equilibrium is obtained by both theoretical analysis and simulation results.Öğe Dynamical Transmission of Coronavirus Model with Analysis and Simulation(Tech Science Press, 2021) Farman, Muhammad; Akgul, Ali; Ahmad, Aqeel; Baleanu, Dumitru; Saleem, Muhammad UmerCOVID-19 acts as a serious challenge to the whole world. Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease. We analyze the diseases free and endemic equilibrium point including stability of the model. The certain threshold value of the basic reproduction number R-0 is found to observe whether population is in disease free state or endemic state. Moreover, the epidemic peak has been obtained and we expect a considerable number of cases. Finally, some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.Öğe Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects(Tech Science Press, 2021) Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Naeem, Muhammad; Baleanu, DumitruToday, coronavirus appears as a serious challenge to the whole world. Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis. New data on COVID-19 are available daily, yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited, and uncertainty remains around nearly all its parameters' values. This research provides the scientific and public health communities better resources, knowledge, and tools to improve their ability to control the infectious diseases. Using the publicly available data on the ongoing pandemic, the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections. Formulation of the testing hypotheses for different countries with a 95% level of confidence, and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries. The results will be helpful in decision making as well as in further mathematical analysis and control strategy. Statistical tools are used to investigate this pandemic, which will be useful for further research. The testing of the hypothesis is done for the differences in various effects including standard errors. Changes in states' variables are observed over time. The rapid outbreak of coronavirus can be stopped by reducing its transmission. Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.Öğe Fractional order age dependent Covid-19 model: An equilibria and quantitative analysis with modeling(Elsevier, 2023) Jamil, Saba; Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Hincal, Evren; El Din, Sayed M.The presence of different age groups in the populations being studied requires us to develop models that account for varying susceptibilities based on age. This complexity adds a layer of difficulty to predicting outcomes accurately. Essentially, there are three main age categories: 0 - 19 years, 20 - 64 years, and > 64 years. However, in this article, we only focus on two age groups (20 - 64 years and > 64 years) because the age category 0 - 19 years is generally perceived as having a lower susceptibility to the virus due to its consistently low infection rate during the pandemic period of this research, particularly in the countries being examined. In this paper, we presented an age-dependent epidemic model for the COVID-19 Outbreak in Kuwait, France, and Cameroon in the fractal-fractional (FF) sense of derivative with the Mittag-Leffler kernel. The study includes positivity, stability, existence results, uniqueness, stability, and numerical simulations. Globally, the age-dependent COVID-19 fractal fractional model is examined using the first and second derivatives of Lyapunov. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model. The numerical scheme of this paper is based on the Newton polynomial and is tested for a particular case with numerical values from Kuwait, France, and Cameroon. In our analysis, we explore the significance of these distinct parameters incorporated into the model, focusing particularly on the impact of vaccination and fractional order on the progression of the epidemic. The results are getting closer to the classical case for the orders reaching 1 while all other solutions are different with the same behavior. Consequently, the fractal fractional order model provides more substantial insights into the epidemic disease. We open a novel viewpoint on enhancing an age-dependent model and applying it to real-world data and parameters. Such a study will help determine the behavior of the virus and disease control methods for a population.Öğe Generalization method of generating the continuous nested distributions(Walter De Gruyter Gmbh, 2023) Farooq, Mian Muhammad; Mohsin, Muhammad; Farman, Muhammad; Akgul, Ali; Saleem, Muhammad UmerIn many life time scenarios, life of one component or system nested in other components or systems. To model these complex structures some so called nested models are required rather than conventional models. This paper introduces the generalization of the method of generating continuous distribution proposed by N. Eugene, C. Lee, and F. Famoye, Beta-normal distribution and its applications, Commun. Stat. Theor. Methods, vol. 31, no. 4, pp. 497-512, 2002 and A. Alzaatreh, C. Lee, and F. Famoye, A new method for generating families of continuous distributions, Metron, vol. 71, no. 1, pp. 63-79, 2013 which nest one model in other to cope with complex systems. Some important characteristics of the proposed family of generalized distribution have been studied. The famous Beta, Kumaraswami and Gamma generated distributions are special cases of our suggested procedure. Some new distributions have also been developed by using the suggested methodology and their important properties have been discussed as well. A variety of real life data sets are used to demonstrate the efficacy of new suggested distributions and illation is made with baseline models.Öğe Modeling and analysis of computer virus fractional order model(Elsevier, 2022) Farman, Muhammad; Akgül, Ali; Ahmad, Aqeel; Saleem, Muhammad Umer; Ahmad, M.O.The aim of this chapter is to analyze the fractional order computer virus epidemic model using the Caputo-Fabrizio and Atangana-Baleanu sense. The existence and uniqueness of the given system of solutions are verified by using the fixed-point theory as well as the iterative method. Graphical results are obtained by using novel numerical procedures to check the negative impact of viruses on a computer as well as to understand the further control strategies. © 2022 Elsevier Inc. All rights reserved.Öğe Modeling and numerical investigation of fractional-order bovine babesiosis disease(Wiley, 2021) Ahmad, Aqeel; Farman, Muhammad; Naik, Parvaiz Ahmad; Zafar, Nayab; Akgul, Ali; Saleem, Muhammad UmerIn this paper, analysis and modeling of bovine babesiosis disease are designed with fractional calculus. The solution for a bovine babesiosis disease and tick populations fractional order system is determined using the Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, the analytical solution of the bovine babesiosis disease has obtained. Furthermore, using an iterative scheme by the Laplace transform, and the Atangana-Baleanu fractional integral, special solutions of the model are obtained. Uniqueness and existence of the solutions by the fixed-point theorem and Picard-Lindel of approach are studied. Numerical simulation has been established for both Caputo and ABC fractional derivative of the proposed system is carried out. The numeric replications for diverse consequences are carried out, and data attained are in good agreement with theoretical outcomes, displaying a vital perception about the use of the set of fractional coupled differential equations to model babesiosis disease and tick populations.Öğe Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator(Nature Portfolio, 2024) Jamil, Saba; Bariq, Abdul; Farman, Muhammad; Nisar, Kottakkaran Sooppy; Akguel, Ali; Saleem, Muhammad UmerRespiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.Öğe Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator (vol 14, 2175, 2024)(Nature Portfolio, 2024) Jamil, Saba; Bariq, Abdul; Farman, Muhammad; Nisar, Kottakkaran Sooppy; Akguel, Ali; Saleem, Muhammad Umer[Abstract Not Available]Öğe SIMULATIONS AND ANALYSIS OF COVID-19 AS A FRACTIONAL MODEL WITH DIFFERENT KERNELS(World Scientific Publ Co Pte Ltd, 2023) Yao, Shao-wen; Farman, Muhammad; Akgul, Ali; Nisar, Kottakkaran Sooppy; Amin, Maryam; Saleem, Muhammad Umer; Inc, MustafaRecently, Atangana proposed new operators by combining fractional and fractal calculus. These recently proposed operators, referred to as fractal-fractional operators, have been widely used to study complex dynamics. In this paper, the COVID-19 model is considered via Atangana-Baleanu fractal-fractional operator. The Lyapunov stability for the model is derived for first and second derivative. Numerical results have developed through Lagrangian-piecewise interpolation for the different fractal-fractional operators. We develop numerical outcomes through different differential and integral fractional operators like power-law, exponential law, and Mittag-Leffler kernel. To get a better outcome of the proposed scheme, numerical simulation is made with different kernels having the memory effects with fractional parameters.
