Browsing by Author "Raza, Ali"

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Numerical Analysis for the Effect of Irresponsible Immigrants on Hiv/Aids Dynamics
(Tech Science Press, 2023) Baleanu, Dumitru; Rafiq, Muhammad; Awrejcewicz, Jan; Ahmed, Nauman; Raza, Ali; Ahmad, Muhammad Ozair; Ali, Muhammad Tariq
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 Susceptible-Infected-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 - WoS: 17
Citation - Scopus: 21
Modeling the Transmission Dynamics of Delayed Pneumonia-Like Diseases With a Sensitivity of Parameters
(Springer, 2021) Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Soori, Atif Hassan; Mohsin, Muhammad; Naveed, Muhammad
Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.
Citation - WoS: 12
Citation - Scopus: 12
Numerical Simulations for Stochastic Meme Epidemic Model
(Springer, 2020) Rafiq, Muhammad; Baleanu, Dumitru; Arif, Muhammad Shoaib; Raza, Ali
The primary purpose of this study is to perform the comparison of deterministic and stochastic modeling. The effect of threshold number is also observed in this model. For numerical simulations, we have developed some stochastic explicit approaches, but they are dependent on time step size. The implicitly driven explicit approach has been developed for a stochastic meme model. The proposed approach is always independent of time step size. Also, we have presented theorems in support of convergence of the proposed approach for the stochastic meme model.
Citation - WoS: 31
Citation - Scopus: 29
Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model
(Tech Science Press, 2020) Baleanu, Dumitru; Rafiq, Muhammad; Raza, Ali; Soori, Atif Hassan; Ahmed, Nauman; Naveed, Muhammad
Mathematical delay modelling has a significant role in the different disciplines such as behavioural, social, physical, biological engineering, and bio-mathematical sciences. The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus (COVID-19). Due to the unavailability of vaccines for the coronavirus worldwide, delay factors such as social distance, quarantine, travel restrictions, extended holidays, hospitalization, and isolation have contributed to controlling the coronavirus epidemic. We have analysed the reproduction number and its sensitivity to parameters. If, Rcovid 1 then this situation will help to eradicate the disease and if, Rcovid 1 the virus will spread rapidly in the human beings. Well-known theorems such as Routh Hurwitz criteria and Lasalle invariance principle have presented for stability. The local and global stabilizes for both equilibria of the model have also been presented. Also, we have analysed the effect of delay reason on the reproduction number. In the last, some very useful numerical consequences have presented in support of hypothetical analysis.
Citation - WoS: 1
Citation - Scopus: 1
Optimization of Coronavirus Pandemic Model Through Artificial Intelligence
(Tech Science Press, 2023) Nasir, Arooj; Baleanu, Dumitru; Raza, Ali; Cheema, Tahir Nawaz; Ahmed, Nauman; Mahmoud, Emad E.; Alqarni, Manal. M.
Artificial intelligence is demonstrated by machines, unlike the natural intelligence displayed by animals, including humans. Artificial intelligence research has been defined as the field of study of intelligent agents, which refers to any system that perceives its environment and takes actions that maximize its chance of achieving its goals. The techniques of intelligent computing solve many applications of mathematical modeling. The research work was designed via a particular method of artificial neural networks to solve the mathematical model of coronavirus. The representation of the mathematical model is made via systems of nonlinear ordinary differential equations. These differential equations are established by collecting the susceptible, the exposed, the symptomatic, super spreaders, infection with asymptomatic, hospitalized, recovery, and fatality classes. The generation of the coronavirus model's dataset is exploited by the strength of the explicit Runge Kutta method for different countries like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, validation, and testing processes for each cyclic update in Bayesian Regularization Backpropagation for the numerical treatment of the dynamics of the desired model. The performance and effectiveness of the designed methodology are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis.
Citation - WoS: 3
Citation - Scopus: 3
Examination of Pine Wilt Epidemic Model Through Efficient Algorithm
(Tech Science Press, 2022) Mahmoud, Emad E.; Al-Bugami, A. M.; Baleanu, Dumitru; Rafiq, Muhammad; Mohsin, Muhammad; Al Nuwairan, Muneerah; Raza, Ali
Pine wilt is a dramatic disease that kills infected trees within a few weeks to a few months. The cause is the pathogen Pinewood Nematode. Most plant-parasitic nematodes are attached to plant roots, but pinewood nematodes are found in the tops of trees. Nematodes kill the tree by feeding the cells around the resin ducts. The modeling of a pine wilt disease is based on six compartments, including three for plants (susceptible trees, exposed trees, and infected trees) and the other for the beetles (susceptible beetles, exposed beetles, and infected beetles). The deterministic modeling, along with subpopulations, is based on Law of mass action. The stability of the model along with equilibria is studied rigorously. The authentication of analytical results is examined through well-known computer methods like Non-standard finite difference (NSFD) and the model's feasible properties (positivity, boundedness, and dynamical consistency). In the end, comparison analysis shows the effectiveness of the NSFD algorithm.
Citation - WoS: 13
Citation - Scopus: 12
Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model
(Mdpi, 2022) Macias-Diaz, Jorge E.; Raza, Ali; Baleanu, Dumitru; Rafiq, Muhammad; Iqbal, Zafar; Ahmad, Muhammad Ozair; Ahmed, Nauman
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, R-0, 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 R-0 < 1. A similar result is obtained for the endemic equilibrium when R-0 > 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 - WoS: 8
Citation - Scopus: 8
Optimality of Solution With Numerical Investigation for Coronavirus Epidemic Model
(Tech Science Press, 2021) Baleanu, Dumitru; Ahmed, Nauman; Shaikh, Tahira Sumbal; Raza, Ali; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur; Shahid, Naveed
The novel coronavirus disease, coined as COVID-19, is a murderous and infectious disease initiated from Wuhan, China. This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far. In this article, the spatio-temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed. To counteract these types of diseases or restrict their spread, mankind depends upon mathematical modeling and medicine to reduce, alleviate, and anticipate the behavior of disease dynamics. The existence and uniqueness of the solution for the proposed system are investigated. Also, the solution to the considered system is made possible in a well-known functions space. For this purpose, a Banach space of function is chosen and the solutions are optimized in the closed and convex subset of the space. The essential explicit estimates for the solutions are investigated for the associated auxiliary data. The numerical solution and its analysis are the crux of this study. Moreover, the consistency, stability, and positivity are the indispensable and core properties of the compartmental models that a numerical design must possess. To this end, a nonstandard finite difference numerical scheme is developed to find the numerical solutions which preserve the structural properties of the continuous system. The M-matrix theory is applied to prove the positivity of the design. The results for the consistency and stability of the design are also presented in this study. The plausibility of the projected scheme is indicated by an appropriate example. Computer simulations are also exhibited to conclude the results.
Citation - WoS: 15
Design and Numerical Analysis of Fuzzy Nonstandard Computational Methods for the Solution of Rumor Based Fuzzy Epidemic Model
(Elsevier, 2022) Rafiq, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Raza, Ali; Ahmad, Muhammad Ozair; Iqbal, Muhammad; Dayan, Fazal
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. (c) 2022 Elsevier B.V. All rights reserved.
Citation - WoS: 28
Citation - Scopus: 32
New Applications Related To Covid-19
(Elsevier, 2021) Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Akgul, Ali
Analysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.
Citation - WoS: 3
Citation - Scopus: 9
Artificial Intelligence Computing Analysis of Fractional Order Covid-19 Epidemic Model
(Aip Publishing, 2023) Baleanu, Dumitru; Cheema, Tahir Nawaz; Fadhal, Emad; Ibrahim, Rashid I. H.; Abdelli, Nouara; Raza, Ali
Artificial intelligence plays a very prominent role in many fields, and of late, this term has been gaining much more popularity due to recent advances in machine learning. Machine learning is a sphere of artificial intelligence where machines are responsible for doing daily chores and are believed to be more intelligent than humans. Furthermore, artificial intelligence is significant in behavioral, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Fractional-order modeling of a real-world problem is a powerful tool for understanding the dynamics of the problem. In this study, an investigation into a fractional-order epidemic model of the novel coronavirus (COVID-19) is presented using intelligent computing through Bayesian-regularization backpropagation networks (BRBFNs). The designed BRBFNs are exploited to predict the transmission dynamics of COVID-19 disease by taking the dataset from a fractional numerical method based on the Grunwald-Letnikov backward finite difference. The datasets for the fractional-order mathematical model of COVID-19 for Wuhan and Karachi metropolitan cities are trained with BRBFNs for biased and unbiased input and target values. The proposed technique (BRBFNs) is implemented to estimate the integer and fractional-order COVID-19 spread dynamics. Its reliability, effectiveness, and validation are verified through consistently achieved accuracy metrics that depend on error histograms, regression studies, and mean squared error.
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.
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.
Citation - WoS: 4
Citation - Scopus: 4
Computational Analysis for Computer Network Model With Fuzziness
(Tech Science Press, 2023) Baleanu, Dumitru; Dayan, Fazal; Ullah, Sami; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; Alfwzan, Wafa F.
A susceptible, exposed, infectious, quarantined and recovered (SEIQR) model with fuzzy parameters is studied in this work. Fuzziness in the model arises due to the different degrees of susceptibility, exposure, infectivity, quarantine and recovery among the computers under consideration due to the different sizes, models, spare parts, the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus, etc. Each individual PC has a different degree of infectivity and resistance against infection. In this scenario, the fuzzy model has richer dynamics than its classical counterpart in epidemiology. The reproduction number of the developed model is studied and the equilibrium analysis is performed. Two different techniques are employed to solve the model numerically. Numerical simulations are performed and the obtained results are compared. Positivity and convergence are maintained by the suggested technique which are the main features of the epidemic models.
Bio-Inspired Modelling of Disease Through Delayed Strategies
(Tech Science Press, 2022) Baleanu, Dumitru; Raza, Ali; Anwar, Pervez; Ahmed, Nauman; Rafiq, Muhammad; Cheema, Tahir Nawaz; Nasir, Arooj
In 2020, the reported cases were 0.12 million in the six regions to the official report of the World Health Organization (WHO). For most children infected with leprosy, 0.008629 million cases were detected under fifteen. The total infected ratio of the children population is approximately 4.4 million. Due to the COVID-19 pandemic, the awareness programs implementation has been disturbed. Leprosy disease still has a threat and puts people in danger. Nonlinear delayed modeling is critical in various allied sciences, including computational biology, computational chemistry, computational physics, and computational economics, to name a few. The time delay effect in treating leprosy delayed epidemic model is investigated. The whole population is divided into four groups: those who are susceptible, those who have been exposed, those who have been infected, and those who have been vaccinated. The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven. The parameters' sensitivity is also examined. The analytical analysis is supported by computer results that are presented in a variety of ways. The proposed approach in this paper preserves equilibrium points and their stabilities, the existence and uniqueness of solutions, and the computational ease of implementation.
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.
Citation - WoS: 4
Citation - Scopus: 3
Evolutionary Computational Method for Tuberculosis Model With Fuzziness
(Aip Publishing, 2023) Dayan, Fazal; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Raza, Ali; Alsaadi, Ateq
This work investigates the computational study of a six-compartmental mathematical model of tuberculosis disease dynamics with the impact of vaccination. Traditional mathematical models presume that all variables are precise and can be measured or calculated precisely. However, in many real-world scenarios, variables may need to be more accurate or easier to quantify, resulting in model uncertainty. Considering this, fuzziness is introduced into the model by taking the contact, recovery, and death rates due to disease as fuzzy membership functions. Two numerical computational schemes, forward Euler and nonstandard finite difference (NSFD), are designed to solve the model. The positivity and convergence for the developed method are investigated, which are significant characteristics of these dynamical models, and it is revealed that these features are preserved in the extended scheme. Numerical computations are performed to support the analytical results. The numerical and computational results indicate that the proposed NSFD method adequately represents the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to design and develop control strategies to support decision-making.
Citation - WoS: 12
Citation - Scopus: 15
Numerical Study of Computer Virus Reaction Diffusion Epidemic Model
(Tech Science Press, 2021) Baleanu, Dumitru; Ahmed, Nauman; Azam, Shumaila; Raza, Ali; Rafiq, Muhammad; Rehman, Muhammad Aziz-ur; Fatima, Umbreen
Reaction-diffusion systems are mathematical models which link to several physical phenomena. The most common is the change in space and time of the meditation of one or more materials. Reaction-diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases. We investigated the transmission dynamics of the computer virus in which connected to each other through network globally. The current study devoted to the structure -preserving analysis of the computer propagation model. This manuscript is devoted to finding the numerical investigation of the reaction-diffusion computer virus epidemic model with the help of a reliable technique. The designed technique is finite difference scheme which sustains the important physical behavior of continuous model like the positivity of the dependent variables, the stability of the equilibria. The theoretical analysis of the proposed method like the positivity of the approximation, stability, and consistency is discussed in detail. A numerical example of simulations yields the authentication of the theoretical results of the designed technique.
Citation - WoS: 4
Citation - Scopus: 4
Stochastic Analysis for the Dynamics of a Poliovirus Epidemic Model
(Tech Science Press, 2022) Baleanu, Dumitru; Khan, Zafar Ullah; Mohsin, Muhammad; Ahmed, Nauman; Rafiq, Muhammad; Anwar, Pervez; Raza, Ali
Most developing countries such as Afghanistan, Pakistan, India, Bangladesh, and many more are still fighting against poliovirus. According to the World Health Organization, approximately eighteen million people have been infected with poliovirus in the last two decades. In Asia, still, some countries are suffering from the virus. The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied. Some basic properties of the deterministic model are studied, equilibria, local stability around the stead states, and reproduction number. Euler Maruyama, stochastic Euler, and stochastic Runge-Kutta study the behavior of complex stochastic differential equations. The main target of this study is to develop a nonstandard computational method that restores dynamical features like positivity, boundedness, and dynamical consistency. Unfortunately, the existing methods failed to fix the actual behavior of the disease. The comparison of the proposed approach with existing methods is investigated.
Citation - Scopus: 1
Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment
(Tech Science Press, 2023) Baleanu, Dumitru; Ahmed, Nauman; Awrejcewicz, Jan; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; Dayan, Fazal
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 beta and delta, 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.