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Boundedness and Positivity Preserving Numerical Analysis of a Fuzzy-Parameterized Delayed Model for Foot and Mouth Disease Dynamics

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Computer Modeling in Engineering & Sciences 2024年第12期141卷 2527-2554页

作者： Muhammad Tashfeen fazal dayan Muhammad Aziz ur Rehman Thabet Abdeljawad Aiman Mukheimer Department of Mathematics School of ScienceUniversity of Management and TechnologyLahore54000Pakistan Department of Mathematics and Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan Department of Mathematics and Applied Mathematics School of Science and TechnologySefakoMakgatho Health Sciences UniversityGa-Rankuwa0208South Africa Center for Applied Mathematics and Bioinformatics(CAMB) Gulf University for Science and TechnologyHawally32093Kuwait

Foot-and-mouth disease(FMD)is a viral disease that affects cloven-hoofed animals including cattle,pigs,and sheep,hence causing export bans among others,causing high economic losses due to reduced *** global effect of FMD is most felt where livestock rearing forms an important source of *** is therefore important to understand the modes of transmission of FMD to control its spread and prevent its *** work intends to address these dynamics by including the efficacy of active migrant animals transporting the disease from one area to another in a fuzzy mathematical modeling *** models of epidemics are determinable with a set of deterministic parameters and this does not reflect on real-life scenarios as observed in *** theory is used in this model as it permits the inclusion of uncertainties in the model;this makes the model more of a reality regarding disease transmission.A time lag,in this case,denotes the incubation period and other time-related factors affecting the spread of FMD and,therefore,is added to the current model for *** that purpose,the analysis of steady states and the basic reproduction number are performed and,in addition,the stability checks are conveyed in the fuzzy *** the numerical solution of the model,we derive the Forward Euler Method and the fuzzy delayed non-standard finite difference(FDNSFD)*** studies of the FDNSFD scheme are performed for convergence,non-negativity,boundedness,and consistency analysis of the numerical projection to guarantee that the numerical model is an accurate discretization of the continuous dynamics of FMD transmission over *** the following simulation study,we show that the FDNSFD method preserves the characteristics of the constant model and still works if relatively large time steps are employed;this is a bonus over the normal finite difference *** study shows how valuable it is to adopt fuzzy theory and time delays whe

关键词： FMD Virus delay epidemic model fuzzy parameters stability consistency

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Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

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Computers, Materials & Continua 2023年第5期75卷 4175-4189页

作者： Dumitru Baleanu fazal dayan Nauman Ahmed Muhammad Rafiq Ali Raza Muhammad Ozair Ahmad Department of Mathematics Cankaya UniversityBalgatAnkara06530Turkey Department of Medical Research China Medical UniversityTaichung406040Taiwan Department of Computer Science and Mathematics Lebanese American UniversityBeirutLebanon Department of Mathematics School of ScienceUniversity of Management and TechnologyLahore54000Pakistan Department of Mathematics and Statistics University of LahoreLahore54590Pakistan Department of Mathematics Faculty of Science and TechnologyUniversity of Central PunjabLahore54000Pakistan Near East University Mathematics Research CenterDepartment of MathematicsNear East Boulevard99138Nicosia/Mersin 10Turkey Department of Mathematics Govt.Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore54000Pakistan

The first major outbreak of the severely complicated hand,foot and mouth disease(HFMD),primarily caused by enterovirus 71,was reported in Taiwan in *** surveillance is needed to assess the spread of *** parameters we use in mathematical models are usually classical mathematical parameters,called crisp parameters,which are taken for *** any biological or physical phenomenon is best explained by *** represent a realistic situation in any mathematical model,fuzzy parameters can be very *** articles have been published on how to control and prevent HFMD from the perspective of public health and statistical ***,few works use fuzzy theory in building models to *** this context,we examined anHFMD model with fuzzy parameters.A Non Standard Finite Difference(NSFD)scheme is developed to solve the *** developed technique retains essential properties such as positivity and dynamic *** simulations are presented to support the analytical *** convergence and consistency of the proposed method are also *** proposed method converges unconditionally while the many classical methods in the literature do not possess this *** this regard,our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

关键词： Hand foot mouth disease fuzzy parameters NSFD scheme convergence consistency

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A Dynamical Study of Modeling the Transmission of Typhoid Fever throughDelayed Strategies

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Computer Modeling in Engineering & Sciences 2024年第11期141卷 1419-1446页

作者： Muhammad Tashfeen fazal dayan Muhammad Aziz Ur Rehman Thabet Abdeljawad Aiman Mukheimer Department of Mathematics School of ScienceUniversity of Management and TechnologyLahore54000Pakistan Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402TaiwanChina Department of Mathematics and Applied Mathematics School of Science and TechnologySefakoMakgatho Health Sciences UniversityGa-Rankuwa0208South Africa Center for Applied Mathematics and Bioinformatics(CAMB) Gulf University for Science and TechnologyHawally32093Kuwait

This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model thathighlights the significance of delay in its *** delays can affect the nature of patterns and slow downthe emergence of patterns in infected population *** analyzed model is expanded with the equilibriumanalysis,reproduction number,and stability *** study aims to establish and explore the non-standardfinite difference(NSFD)scheme for the typhoid fever virus transmission model with a time *** addition,the forward Euler method and Runge-Kutta method of order 4(RK-4)are also applied in the present *** significant properties,such as convergence,positivity,boundedness,and consistency,are explored,and theproposed scheme preserves all the mentioned *** theoretical validation is conducted on how NSFDoutperforms other methods in emulating key aspects of the continuous model,such as positive solution,stability,and equilibrium about ***,the above analysis also shows some of the limitations of the conventional finitedifference methods,such as forward Euler and RK-4 in simulating such critical *** becomes moreapparent when using larger *** indicated that NSFD is beneficial in identifying the essential characteristicsof the continuous model with higher accuracy than the traditional approaches.

关键词： Typhoid virus delay epidemic model stability consistency global stability

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Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment

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Computers, Materials & Continua 2023年第2期74卷 2345-2361页

作者： fazal dayan Dumitru Baleanu Nauman Ahmed Jan Awrejcewicz Muhammad Rafiq Ali Raza Muhammad Ozair Ahmad Department of Mathematics School of ScienceUniversity of Management and TechnologyLahore54000Pakistan Department of Mathematics Cankaya UniversityBalgatAnkara06530Turkey Department of Medical Research China Medical UniversityTaichung40402Taiwan Institute of Space Sciences Magurele-Bucharest077125Romania Department of Mathematics and Statistics University of LahoreLahore54000Pakistan Department of Automation Biomechanics and MechatronicsLodz University of Technology1/15 Stefanowskiego St.90-924LodzPoland Department of Mathematics Faculty of Science&TechnologyUniversity of Central PunjabLahore54000Pakistan Department of Mathematics Govt.Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore54000Pakistan

The application of fuzzy theory is vital in all scientific *** construction of mathematical models with fuzziness is little studied in the *** 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 classicalmodel ofmalaria *** parametersβandδ,being function of the malaria virus load,are considered fuzzy *** 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 ***,numerical simulations are carried out to illustrate the analytical results of the developed *** 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.

关键词： SIER model fuzzy parameters malaria NSFD scheme stability

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A Nonstandard Computational Investigation of SEIR Model with Fuzzy Transmission, Recovery and Death Rates

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Computers, Materials & Continua 2023年第11期77卷 2251-2269页

作者： Ahmed H.Msmali fazal dayan Muhammad Rafiq Nauman Ahmed Abdullah Ali H.Ahmadini Hassan A.Hamali Department of Mathematics College of ScienceJazan UniversityJazan45142Saudi Arabia Department of Mathematics School of ScienceUniversity of Management and TechnologyLahorePakistan Department of Mathematics Faculty of Science&TechnologyUniversity of Central PunjabLahorePakistan Department of Mathematics and Statistics University of LahoreLahorePakistan Department of Medical Laboratory Technology Faculty of Applied Medical SciencesJazan UniversityP.O.Box 1906Jazan45142Saudi Arabia

In this article,a Susceptible-Exposed-Infectious-Recovered(SEIR)epidemic model is *** equilibrium analysis and reproduction number are *** conventional models have made assumptions of homogeneity in disease transmission that contradict the actual ***,it is crucial to consider the heterogeneity of the transmission rate when modeling disease *** the heterogeneity of disease transmission mathematically can be achieved by incorporating fuzzy theory.A numerical scheme nonstandard,finite difference(NSFD)approach is developed for the studied model and the results of numerical simulations are *** of the constructed scheme are *** positivity,convergence and consistency of the developed technique are investigated using mathematical induction,Jacobean matrix and Taylor series expansions *** suggested scheme preserves all these essential characteristics of the disease dynamical *** numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the ***,the obtained method generates plausible predictions that can be used by regulators to support the decision-making process to design and develop control *** of the natural immunity on the infected class are studied which reveals that an increase in natural immunity can decrease the infection and vice versa.

关键词： Epidemic model fuzzy parameters NSFD scheme convergence positivity consistency

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Computational Analysis for Computer Network Model with Fuzziness

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Intelligent Automation & Soft Computing 2023年第8期37卷 1909-1924页

作者： Wafa F.Alfwzan Dumitru Baleanu fazal dayan Sami Ullah Nauman Ahmed Muhammad Rafiq Ali Raza Department of Mathematical Sciences College of SciencePrincess Nourah bint Abdulrahman UniversityP.O.Box 84428Riyadh11671Saudi Arabia Department of Mathematics Cankaya UniversityBalgatAnkara06530Turkey Institute of Space Sciences Magurele-Bucharest077125Romania Department of Computer Science and Mathematics Lebanese American UniversityBeirutLebanon Department of Mathematics School of ScienceUniversity of Management and TechnologyLahore54000Pakistan Department of Mathematics and Statistics University of LahoreLahore54590Pakistan Department of Mathematics Faculty of Science and TechnologyUniversity of Central PunjabLahore54000Pakistan Near East University Mathematics Research CenterDepartment of MathematicsNear East BoulevardPC:99138Nicosia/Mersin 10Turkey Department of Mathematics Govt.Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore54000Pakistan

A susceptible,exposed,infectious,quarantined and recovered(SEIQR)model with fuzzy parameters is studied in this *** 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,*** individual PC has a different degree of infectivity and resis-tance against *** this scenario,the fuzzy model has richer dynamics than its classical counterpart in *** reproduction number of the developed model is studied and the equilibrium analysis is *** different techniques are employed to solve the model *** simulations are performed and the obtained results are *** and convergence are maintained by the suggested technique which are the main features of the epidemic models.

关键词： NSFD method computer virus fuzzy parameters convergence stability

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Bio-Inspired Numerical Analysis of COVID-19 with Fuzzy Parameters

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Computers, Materials & Continua 2022年第8期72卷 3213-3229页

作者： F.M.Allehiany fazal dayan F.F.Al-Harbi Nesreen Althobaiti Nauman Ahmed Muhammad Rafiq Ali Raza Mawahib Elamin Department of Mathematical Sciences College of Applied SciencesUmm Al-Qura UniversityMakkah21955Saudi Arabia Department of Mathematics and Statistics University of LahoreLahorePakistan Department of Mathematics School of ScienceUniversity of Management and TechnologyLahorePakistan Department of Physics College of SciencePrincess Nourah Bint Abdulrahman UniversityRiyadh11671Saudi Arabia Department of Mathematics and Statistics College of ScienceTaif UniversityTaif21944Saudi Arabia Department of Mathematics Faculty of SciencesUniversity of Central PunjabLahorePakistan Department of Mathematics Govt.Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore54000Pakistan Department of Mathematics College of Science and ArtsQassim UniversityRiyadh Al KhabraSaudi Arabia

Fuzziness or uncertainties arise due to insufficient knowledge,experimental errors,operating conditions and parameters that provide inaccurate *** concepts of susceptible,infectious and recovered are uncertain due to the different degrees in susceptibility,infectivity and recovery among the individuals of the *** differences can arise,when the population groups under the consideration having distinct habits,customs and different age groups have different degrees of resistance,*** realistic models are needed which consider these different degrees of susceptibility infectivity and recovery of the *** this paper,a Susceptible,Infected and Recovered(SIR)epidemic model with fuzzy parameters is *** infection,recovery and death rates due to the disease are considered as fuzzy *** basic reproduction number and fuzzy equilibrium points have been derived for the studied *** is then solved numerically with three different techniques,forward Euler,Runge-Kutta fourth order method(RK-4)and the nonstandard finite difference(NSFD)methods *** NSFD technique becomes more efficient and reliable among the others and preserves all the essential features of a continuous dynamical system.

关键词： Fuzzy parameters SIR model NSFD scheme fuzzy equilibrium points fuzzy stability analysis

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Modeling of Computer Virus Propagation with Fuzzy Parameters

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Computers, Materials & Continua 2023年第3期74卷 5663-5678页

作者： Reemah M.Alhebshi Nauman Ahmed Dumitru Baleanu Umbreen Fatima fazal dayan Muhammad Rafiq Ali Raza Muhammad Ozair Ahmad Emad E.Mahmoud Computer Science Department Faculty of Computing and Information TechnologyKing Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics and Statistics University of LahoreLahore54590Pakistan Department of Mathematics Cankaya UniversityBalgatAnkara06530Turkey Department of Medical Research China Medical UniversityTaichung406040TaiwanChina Institute of Space Sciences Magurele-Bucharest077125Romania Department of Computer Science University of LahoreLahore54590Pakistan Department of Mathematics School of ScienceUniversity of Management and TechnologyLahore54000Pakistan Department of Mathematics Faculty of Science and TechnologyUniversity of Central PunjabLahore54000Pakistan Department of Mathematics Near East University TRNCMersin10Turkey Department of Mathematics Government Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore5400Pakistan Department of Mathematics and Statistics College of ScienceTaif UniversityP O Box11099Taif21944Saudi Arabia

Typically,a computer has infectivity as soon as it is *** is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the *** understand the dynamics of the virus propagation in a better way,a computer virus spread model with fuzzy parameters is presented in this *** 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 *** this,the parametersβandγbeing functions of the computer virus load,are considered fuzzy *** fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical *** essential features of the model,like reproduction number and equilibrium analysis,are discussed in fuzzy ***,with fuzziness,two numerical methods,the forward Euler technique,and a nonstandard finite difference(NSFD)scheme,respectively,are developed and *** the evidence of the numerical simulations,the proposed NSFD method preserves the main features of the dynamic *** can be considered a reliable tool to predict such types of solutions.

关键词： SIR model fuzzy parameters computer virus NSFD scheme stability

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New Trends in Fuzzy Modeling Through Numerical Techniques

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Computers, Materials & Continua 2023年第3期74卷 6371-6388页

作者： M.M.Alqarni Muhammad Rafiq fazal dayan Jan Awrejcewicz Nauman Ahmed Ali Raza Muhammad Ozair Ahmad Witold Pawłowski Emad E.Mahmoud Department of Mathematics College of SciencesKing Khalid UniversityAbha61413Saudi Arabia Department of Mathematics Faculty of Sciences and TechnologyUniversity of Central PunjabLahorePakistan Department of Mathematics School of ScienceUniversity of Management and TechnologyLahorePakistan Department of Automation Biomechanics and MechatronicsLodz University of Technology1/15 Stefanowskiego St.90-924LodzPoland Department of Mathematics and Statistics University of LahoreLahorePakistan Department of Mathematics Govt.Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore54000Pakistan Institute of Machine Tools and Production Engineering Lodz University of TechnologyPoland Department of Mathematics College of ScienceTaif UniversityP.O.Box11099Taif21944Saudi Arabia

Amoebiasis is a parasitic intestinal infection caused by the highly pathogenic amoeba Entamoeba *** is spread through person-toperson contact or by eating or drinking food or water contaminated with *** transmission rate depends on the number of cysts present in the *** traditional models assumed a homogeneous and contradictory transmission with *** heterogeneity of its transmission rate is a significant factor when modeling disease *** heterogeneity of disease transmission can be described mathematically by introducing fuzzy *** this context,a fuzzy SEIR Amoebiasis disease model is considered in this *** equilibrium analysis and reproductive number are studied with *** numerical schemes forward Euler method and a nonstandard finite difference(NSFD)approach,are developed for the learned model,and the results of numerical simulations are *** numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease despite the uncertainty and ***,the obtained method generates plausible predictions that regulators can use to support decision-making to design and develop control strategies.

关键词： Epidemic model fuzzy parameters amoebiasis NSFD scheme convergence

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