Browsing by Author "Ahmad, Muhammad Ozair"

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Citation Count: Baleanu, Dumitru...et.al. (2023). "Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness", Computers, Materials and Continua, Vol.75, No.2, pp.4175-4189.
Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness
(2023) Baleanu, Dumitru; Dayan, Fazal; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; 56389
The first major outbreak of the severely complicated hand, foot and mouth disease (HFMD), primarily caused by enterovirus 71, was reported in Taiwan in 1998. HFMD surveillance is needed to assess the spread of HFMD. The parameters we use in mathematical models are usually classical mathematical parameters, called crisp parameters, which are taken for granted. But any biological or physical phenomenon is best explained by uncertainty. To represent a realistic situation in any mathematical model, fuzzy parameters can be very useful. Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling. However, few works use fuzzy theory in building models to simulate HFMD dynamics. In this context, we examined an HFMD model with fuzzy parameters. A Non Standard Finite Difference (NSFD) scheme is developed to solve the model. The developed technique retains essential properties such as positivity and dynamic consistency. Numerical simulations are presented to support the analytical results. The convergence and consistency of the proposed method are also discussed. The proposed method converges unconditionally while the many classical methods in the literature do not possess this property. In this regard, our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.
Citation Count: Dayan, Fazal;...et.al. (2022). "Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics", AIMS Mathematics, Vol.7, No.5, pp.8449-8470.
Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics
(2022) Dayan, Fazal; Ahmed, Nauman; Rafiq, Muhammad; Akgül, Ali; Raza, Ali; Ahmad, Muhammad Ozair; Jarad, Fahd; 234808
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.
Citation Count: Dayan, Fazal;...et.al. (2022). "Design and numerical analysis of fuzzy nonstandard computational methods for the solution of rumor based fuzzy epidemic model", Physica A: Statistical Mechanics and its Applications, Vol.600.
Design and numerical analysis of fuzzy nonstandard computational methods for the solution of rumor based fuzzy epidemic model
(2022) Dayan, Fazal; Rafiq, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Raza, Ali; Ahmad, Muhammad Ozair; Iqbal, Muhammad; 56389
This model extends the classical epidemic model for cyber consumerism by introducing fuzziness to the model. Fuzziness arises due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of confused, escapers and recovered consumers are uncertain due to the different degrees of confusion, escaping and recovery among the individuals of the cyber consumers. The differences can arise, when the cyber consumers under the consideration having distinct habits, customs and different age groups have different degrees of resistance, etc. The chance of transmission of rumors and recovery rates are considered as fuzzy numbers. A rumor-free and two rumor existing-endemic equilibrium points have been derived for the studied model. The model is then solved numerically with fuzzy forward Euler and fuzzy nonstandard finite difference (FNSFD) methods respectively. The numerical and simulation results show that the proposed FNSFD technique is an efficient and reliable tool to deal with such type of dynamical system.
Citation Count: Ahmed, Nauman;...et.al. (2022). "Design, analysis and comparison of a nonstandard computational method for the solution of a general stochastic fractional epidemic model", Axioms, Vol.11, No.1.
Design, analysis and comparison of a nonstandard computational method for the solution of a general stochastic fractional epidemic model
(2022) Ahmed, Nauman; Macías-Díaz, Jorge E.; Raza, Ali; Iqbal, Zafar; Ahmad, Muhammad Ozair; Baleanu, Dumitru; Rafiq, Muhammad; 56389
Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0 < 1. A similar result is obtained for the endemic equilibrium when R0 > 1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.
Citation Count: Alhebshi, Reemah M.;...et.al. (2023). "Modeling of Computer Virus Propagation with Fuzzy Parameters", Computers, Materials and Continua, Vol.74, no.3, pp.5663-5678.
Modeling of Computer Virus Propagation with Fuzzy Parameters
(2023) Alhebshi, Reemah M.; Ahmed, Nauman; Baleanu, Dumitru; Fatima, Umbreen; Dayan, Fazal; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; Mahmoud, Emad E.; 56389
Typically, a computer has infectivity as soon as it is infected. It is a reality that no antivirus programming can identify and eliminate all kinds of viruses, suggesting that infections would persevere on the Internet. To understand the dynamics of the virus propagation in a better way, a computer virus spread model with fuzzy parameters is presented in this work. It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity, which depends on the quantity of virus.Considering this, the parameters β and γ being functions of the computer virus load, are considered fuzzy numbers. Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models. The essential features of the model, like reproduction number and equilibrium analysis, are discussed in fuzzy senses.Moreover, with fuzziness, two numerical methods, the forward Euler technique, and a nonstandard finite difference (NSFD) scheme, respectively, are developed and analyzed. In the evidence of the numerical simulations, the proposed NSFD method preserves the main features of the dynamic system. It can be considered a reliable tool to predict such types of solutions.
Citation Count: Ahmed, Nauman;...et.al. (2022). "New applications related to hepatitis C model", AIMS Mathematics, Vol.7, No.6, pp.11362-11381.
New applications related to hepatitis C model
(2022) Ahmed, Nauman; Raza, Ali; Akgül, Ali; Iqbal, Zafar; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Jarad, Fahd; 234808
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 R0 is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if R0 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 R0 < 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.
Citation Count: Ali, Muhammad Tariq;...et.al. (2023). "Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics", Intelligent Automation and Soft Computing, Vol.36, no.2, pp.1479-1496.
Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics
(2023) Ali, Muhammad Tariq; Baleanu, Dumitru; Rafiq, Muhammad; Awrejcewicz, Jan; Ahmed, Nauman; Raza, Ali; Iqbal, Muhammad Sajid; Ahmad, Muhammad Ozair; 56389
The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The SusceptibleInfected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes ‘ℎ’. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease.
Citation Count: Ahmed, Nauman...et al. (2020). "Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model", Frontiers in Physics, Vol. 7.
Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model
(2020) Ahmed, Nauman; Fatima, Mehreen; Baleanu, Dumitru; Nisar, Kottakkaran Soopp; Khan, Ilyas; Rafiq, Muhammad; Rehman, Muhammad Aziz Ur; Ahmad, Muhammad Ozair; 56389
In this paper, two structure-preserving nonstandard finite difference (NSFD) operator splitting schemes are designed for the solution of reaction diffusion epidemic models. The proposed schemes preserve all the essential properties possessed by the continuous systems. These schemes are applied on a diffusive SEIQV epidemic model with a saturated incidence rate to validate the results. Furthermore, the stability of the continuous system is proved, and the bifurcation value is evaluated. A comparison is also made with the existing operator splitting numerical scheme. Simulations are also performed for numerical experiments.
Citation Count: Dayan, Fazal;...et.al. (2023). "Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment", Computers, Materials and Continua, Vol.74, No.2, pp.2345-2361.
Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment
(2023) Dayan, Fazal; Baleanu, Dumitru; Ahmed, Nauman; Awrejcewicz, Jan; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; 56389
The application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classical model of malaria transmission. The parameters β and δ, being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.
Citation Count: Azam, Shumaila...et al. (2021). "Structure preserving numerical scheme for spatio-temporal epidemic model of plant disease dynamics", Results in Physics, Vol. 30.
Structure preserving numerical scheme for spatio-temporal epidemic model of plant disease dynamics
(2021) Azam, Shumaila; Ahmed, Nauman; Akgül, Ali; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Baleanu, Dumitru; 56389
In this article, an implicit numerical design is formulated for finding the numerical solution of spatiotemporal nonlinear dynamical system with advection. Such type of problems arise in many fields of life sciences, mathematics, physics and engineering. The epidemic model describes the population densities that have some special types of features. These features should be maintained by the numerical design. The proposed scheme, not only solves the nonlinear physical system but also preserves the structure of the state variables. Von-Neumann criteria, M-matrix theory and Taylor's expansion are used for proving some standard results. Basic reproduction number is evaluated and its key role in deciding the stability at the equilibrium points is also investigated. Graphical solutions are also presented against the test problem.