Browsing by Author "Rafiq, Muhammad"

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Citation Count: Iqbal, Zafar...et al. (2023). "A finite difference scheme to solve a fractional order epidemic model of computer virus", Aims Mathematics, Vol.8, No. 1, pp.2337-2359.
A finite difference scheme to solve a fractional order epidemic model of computer virus
(2023) Iqbal, Zafar; Rehman, Muhammad Aziz-ur; Imran, Muhammad; Ahmed, Nauman; Fatima, Umbreen; Akgul, Ali; Rafiq, Muhammad; Raza, Ali; Djuraev, Ali Asrorovich; Jarad, Fahd
In this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number R0 functions in stability analysis and illness dynamics.
Citation Count: Rafiq, Muhammad...et al. (2020). "A reliable and competitive mathematical analysis of Ebola epidemic model", Advances in Difference Equations, Vol. 2020, No. 1.
A reliable and competitive mathematical analysis of Ebola epidemic model
(2020) Rafiq, Muhammad; Ahmad, Waheed; Abbas, Mujahid; Baleanu, Dumitru; 56389
The purpose of this article is to discuss the dynamics of the spread of Ebola virus disease (EVD), a kind of fever commonly known as Ebola hemorrhagic fever. It is rare but severe and is considered to be extremely dangerous. Ebola virus transmits to people through domestic and wild animals, called transmitting agents, and then spreads into the human population through close and direct contact among individuals. To study the dynamics and to illustrate the stability pattern of Ebola virus in human population, we have developed an SEIR type model consisting of coupled nonlinear differential equations. These equations provide a good tool to discuss the mode of impact of Ebola virus on the human population through domestic and wild animals. We first formulate the proposed model and obtain the value of threshold parameter R0 for the model. We then determine both the disease-free equilibrium (DFE) and endemic equilibrium (EE) and discuss the stability of the model. We show that both the equilibrium states are locally asymptotically stable. Employing Lyapunov functions theory, global stabilities at both the levels are carried out. We use the Runge-Kutta method of order 4 (RK4) and a non-standard finite difference (NSFD) scheme for the susceptible-exposed-infected-recovered (SEIR) model. In contrast to RK4, which fails for large time step size, it is found that the NSFD scheme preserves the dynamics of the proposed model for any step size used. Numerical results along with the comparison, using different values of step size h, are provided.
Citation Count: Farooqi, Asma...et al. (2020). "An Accurate Predictor-Corrector-Type Nonstandard Finite Difference Scheme for an SEIR Epidemic Model", Journal of Mathematics, Vol. 2020.
An Accurate Predictor-Corrector-Type Nonstandard Finite Difference Scheme for an SEIR Epidemic Model
(2020) Farooqi, Asma; Ahmad, Ria; Farooqi, Rashada; Alharbi, Sayer O.; Baleanu, Dumitru; Rafiq, Muhammad; Khan, Ilyas; Ahmad, M. O.; 56389
The present work deals with the construction, development, and analysis of a viable normalized predictor-corrector-type nonstandard finite difference scheme for the SEIR model concerning the transmission dynamics of measles. The proposed numerical scheme double refines the solution and gives realistic results even for large step sizes, thus making it economical when integrating over long time periods. Moreover, it is dynamically consistent with a continuous system and unconditionally convergent and preserves the positive behavior of the state variables involved in the system. Simulations are performed to guarantee the results, and its effectiveness is compared with well-known numerical methods such as Runge-Kutta (RK) and Euler method of a predictor-corrector type.
Citation Count: Jawaz, Muhammad;...et.al. (2023). "Analysis and numerical effects of time-delayed rabies epidemic model with diffusion", International Journal of Nonlinear Sciences and Numerical Simulation, Vol.24, No.6, pp.2179-2194.
Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
(2023) Jawaz, Muhammad; Rehman, Muhammad Aziz-Ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; 56389
The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von-Neumann method. Taylor's expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of τ on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.
Citation Count: Nasir, Arooj;...et.al. (2022). "Bio-Inspired Modelling of Disease Through Delayed Strategies", Computers, Materials and Continua, Vol.73, No.3, pp.5717-5734.
Bio-Inspired Modelling of Disease Through Delayed Strategies
(2022) Nasir, Arooj; Baleanu, Dumitru; Raza, Ali; Anwar, Pervez; Ahmed, Nauman; Rafiq, Muhammad; Cheema, Tahir Nawaz; 56389
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 Count: Raza, A...et al. (2019). "Competitive Numerical Analysis for Stochastic Hıv/Aıds Epidemic Model in A Two-Sex Population",Iet Systems Biology, Vol. 13, No. 6, pp. 305-315.
Competitive Numerical Analysis for Stochastic Hıv/Aıds Epidemic Model in A Two-Sex Population
(Institution of Engineering and Technology, 2019) Raza, A.; Rafiq, Muhammad; Baleanu, Dumitru; Arif, Muhammed Shoaib; Naveed, Muhammad; Ashraf, Kaleem; 56389
This study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two-sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H* holds on the stochastic HIV/AIDS epidemic model. If H* < 1 then condition helps us to control disease in a two-sex human population while H* > 1 explains the persistence of disease in the two-sex human population. Lamentably, numerical methods such as Euler–Maruyama, stochastic Euler, and stochastic Runge–Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non-standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two-sex population.
Citation Count: Raza, Ali;...et.al. (2022). "Computational algorithms for the analysis of cancer virotherapy model", Computers, Materials and Continua, Vol.71, No.2, pp.3621-3634.
Computational algorithms for the analysis of cancer virotherapy model
(2022) Raza, Ali; Baleanu, Dumitru; Rafiq, Muhammad; Abbas, Syed Zaheer; Siddique, Abubakar; Javed, Umer; Naz, Mehvish; Fatima, Arooj; Munawar, Tayyba; Batool, Hira; Nazir, Zaighum; 56389
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 theWorld 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 cancerlike 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.
Citation Count: Alfwzan, Wafa F...et.al. (2023). "Computational Analysis for Computer Network Model with Fuzziness", Intelligent Automation and Soft Computing, Vol.37, No.2, pp.1909-1924.
Computational Analysis for Computer Network Model with Fuzziness
(2023) Alfwzan, Wafa F.; Baleanu, Dumitru; Dayan, Fazal; Ullah, Sami; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; 56389
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.
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: Alfwzan, Wafa F...et.al. (2023). "Dynamical analysis of a class of SEIR models through delayed strategies", AIP Advances, Vol.13, No.7.
Dynamical analysis of a class of SEIR models through delayed strategies
(2023) Alfwzan, Wafa F.; Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Ahmed, Nauman; 56389
In recent decades, the mathematical modeling of infectious diseases, real-world problems, non-linear dynamical complex systems, etc., has increased significantly. According to World Health Organization, tobacco use is the cause of about 22% of cancer deaths. Another 10% are due to obesity, poor diet, lack of physical activity, and excessive drinking of alcohol. Approximately 5%-10% of cancers are due to inherited genetic defects. The objective is to investigate the impact of time delays in implementing control measures on the epidemic dynamics. The classification of cell population has four compartments: susceptible cells (x), cancer-infected cells (y), virus-free cells (v), and immune cells (z). Our focus is to find the equilibria of the problem and their stability. The stability of the solutions is of two types: locally asymptotic and globally asymptotic. The Routh-Hurwitz criterion, Volterra-type Lyapunov function, and LaSalle’s invariance principle are used to verify the stability of solutions. The graphical behavior depicts the stable solutions to a real-world problem and supports the stability analysis of the problem. The findings contribute to the understanding of epidemic dynamics and provide valuable information for designing and implementing effective intervention strategies in public health systems.
Citation Count: Naveed, Muhammad...et al. (2020). "Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model", CMC-Computers Materials & Continua, Vol. 65, No. 1, pp. 225-241.
Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model
(2020) Naveed, Muhammad; Baleanu, Dumitru; Rafiq, Muhammad; Raza, Ali; Soori, Atif Hassan; Ahmed, Nauman; 56389
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 Count: Alsaadi, Ateq...et.al. (2023). "Evolutionary computational method for tuberculosis model with fuzziness", AIP Advances, Vol.13, No.8.
Evolutionary computational method for tuberculosis model with fuzziness
(2023) Alsaadi, Ateq; Dayan, Fazal; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Raza, Ali; 56389
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 Count: Raza, Ali;...et.al. (2022). "Examination of Pine Wilt Epidemic Model through Efficient Algorithm", Computers, Materials and Continua, Vol.71, No.2, pp.5293-5310.
Examination of Pine Wilt Epidemic Model through Efficient Algorithm
(2022) Raza, Ali; Mahmoud, Emad E.; Al-Bugami, A. M.; Baleanu, Dumitru; Rafiq, Muhammad; Mohsin, Muhammad; Nuwairan, Muneerah Al; 56389
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 Count: Iqbal, Zafar...et al. (2021). "Mathematical and numerical investigations of the fractional-order epidemic model with constant vaccination strategy", Romanian Reports in Physics, Vol. 73, No. 2.
Mathematical and numerical investigations of the fractional-order epidemic model with constant vaccination strategy
(2021) Iqbal, Zafar; Rehman, Muhammad Aziz U; Baleanu, Dumitru; Ahmed, Nauman; Raza, Ali; Rafiq, Muhammad; 56389
This work is devoted to find the reliable numerical solution of an epidemic model with constant vaccination strategy. For this purpose, a structure preserving numerical scheme called the Grünwald-Letnikov nonstandard finite difference scheme is designed. The proposed technique retains all the important properties of the continuous epidemic model like boundedness, positivity, and stability. This behavior of the proposed numerical scheme is validated mathematically and graphically. The role of the vaccination in controlling the disease dynamics in the population is verified through numerical simulations. The stability of the system under discussion is also ex-amined at the disease free equilibrium point and the endemic equilibrium point. Finally, the outcome of this study is furnished with concluding remarks and future directions of research. © 2021, Editura Academiei Romane. All rights reserved.
Citation Count: Raza, Ali...et al. (2022). "Modeling of anthrax disease via efficient computing techniques", Intelligent Automation and Soft Computing, Vol. 32, No. 2, pp. 1109-1124.
Modeling of anthrax disease via efficient computing techniques
(2022) Raza, Ali; Baleanu, Dumitru; Yousaf, Muhammad; Akhter, Naeem; Mahmood, Syed Kashif; Rafiq, Muhammad; 56389
Computer methods have a significant role in the scientific literature. Nowadays, development in computational methods for solving highly complex and nonlinear systems is a hot issue in different disciplines like engineering, physics, biology, and many more. Anthrax is primarily a zoonotic disease in herbivores caused by a bacterium called Bacillus anthracis. Humans generally acquire the disease directly or indirectly from infected animals, or through occupational exposure to infected or contaminated animal products. The outbreak of human anthrax is reported in the Eastern Mediterranean regions like Pakistan, Iran, Iraq, Afghanistan, Morocco, and Sudan. Almost ninety-five percent chances are the transmission of the bacteria from forming spores by the World Health Organization (WHO). The modeling of an anthrax disease is based on the four compartments along with two humans (susceptible and infected) and others are dead bodies and sporing agents. The mathematical analysis is studied along with the fundamental properties of deterministic modeling. The stability of the model along with equilibria is studied rigorously. The authentication of analytical results is examined through well-known computer methods like Euler, Runge Kutta, and Non-standard finite difference (NSFD) along with the feasible properties (positivity, boundedness, and dynamical consistency) of the model. In the end, comparison analysis of algorithms shows the effectiveness of the methods. © 2022, Tech Science Press. All rights reserved.
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: Naveed, Muhammad...et al. (2021). "Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters", Advances in Difference Equations, Vol. 2021, No 1.
Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters
(2021) Naveed, Muhammad; Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Soori, Atif Hassan; Mohsin, Muhammad; 56389
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. © 2021, The Author(s).