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The impact of standard and nonstandard finite difference schemes on HIV nonlinear dynamical model

dc.authorid Asjad, Muhammad Imran/0000-0002-1484-5114
dc.authorscopusid 57987814800
dc.authorscopusid 58399816600
dc.authorscopusid 57916746700
dc.authorscopusid 57897458100
dc.authorscopusid 57925959400
dc.authorscopusid 16318328300
dc.authorscopusid 16318328300
dc.authorwosid Baleanu, Dumitru/B-9936-2012
dc.authorwosid Asjad, Muhammad/X-1799-2019
dc.authorwosid Tag Eldin, Elsayed/Gzb-2017-2022
dc.contributor.author Li, Shuo
dc.contributor.author Bukhsh, Imam
dc.contributor.author Khan, Ihsan Ullah
dc.contributor.author Asjad, Muhammad Imran
dc.contributor.author Eldin, Sayed M.
dc.contributor.author Abd El-Rahman, Magda
dc.contributor.author Baleanu, Dumitru
dc.contributor.authorID 56389 tr_TR
dc.contributor.other Matematik
dc.date.accessioned 2024-01-24T11:54:22Z
dc.date.available 2024-01-24T11:54:22Z
dc.date.issued 2023
dc.department Çankaya University en_US
dc.department-temp [Li, Shuo] Changji Univ, Sch Math & Data Sci, Changji 831100, Xinjiang, Peoples R China; [Bukhsh, Imam; Khan, Ihsan Ullah] Gomal Univ, Inst Numer Sci, Dept Math, Dera Ismail Khan 29050, Kpk, Pakistan; [Asjad, Muhammad Imran] Univ Management & Technol, Dept Math, Lahore 54770, Pakistan; [Eldin, Sayed M.] Future Univ Egypt, Fac Engn, Ctr Res, New Cairo 11835, Egypt; [Abd El-Rahman, Magda] King Khalid Univ, Coll Sci, Dept Phys, Abha 61413, Saudi Arabia; [Baleanu, Dumitru] Cankaya Univ, Dept Math, Ankara, Turkiye en_US
dc.description Asjad, Muhammad Imran/0000-0002-1484-5114 en_US
dc.description.abstract Mathematical models are enormously valuable in recognition the characteristics of infectious afflictions. The present study describes and analyses a nonlinear Susceptible-Infected (S center dot I) type mathematical model for HIV/ AIDS. To better comprehend the dynamics of disease diffusion, it is assumed that by giving AIDS patients timely Anti Retroviral Therapy (ART), their transition into HIV infected class is attainable. The ART treatment can reduce or manage the spread of disease among individuals that can extend their life for some more years. For the model, the basic reproduction number is formed which provides a base to study the stability of disease free and endemic equilibria. To understand the entire dynamical behavior of the model, standard finite difference (SFD) schemes such as Runge-Kutta of order four (RK-4) and forward Euler schemes and nonstandard finite difference (NSFD) scheme are implemented. The goal of constructing the NSFD scheme for differential equations is to ensure that it is dynamically reliable, while maintaining important dynamical properties like the positivity of the solutions and its convergence to equilibria of continuous model for all finite step sizes. However, the essential characteristics of the continuous model cannot be properly maintained by the Euler and RK-4 schemes, leading to the possibility of numerical solutions that are not entirely similar to those of the original model. For the NSFD scheme, the Routh-Hurwitz criterion is used to assess the local stability of disease-free and endemic equilibria. To explain the global stability of both the equilibria, Lyapunov functions are offered. To verify the theoretical findings and validate the dynamical aspects of the abovementioned schemes, numerical simulations are also provided. The outcomes offered in this study may be engaged as an effective tool for forecasting the progression of HIV/AIDS epidemic diseases. en_US
dc.description.publishedMonth 8
dc.description.sponsorship Deanship of Scientific Research at King Khalid University; [RGP2/69/44] en_US
dc.description.sponsorship Magda Abd El-Rahman extends their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under grant number RGP2/69/44. en_US
dc.description.woscitationindex Science Citation Index Expanded
dc.identifier.citation Li, Shuo;...et.al. (2023). "The impact of standard and nonstandard finite difference schemes on HIV nonlinear dynamical model", Chaos, Solitons and Fractals, Vol.173. en_US
dc.identifier.doi 10.1016/j.chaos.2023.113755
dc.identifier.issn 0960-0779
dc.identifier.issn 1873-2887
dc.identifier.scopus 2-s2.0-85163478592
dc.identifier.scopusquality Q1
dc.identifier.uri https://doi.org/10.1016/j.chaos.2023.113755
dc.identifier.volume 173 en_US
dc.identifier.wos WOS:001053704100001
dc.identifier.wosquality Q1
dc.institutionauthor Baleanu, Dumitru
dc.language.iso en en_US
dc.publisher Pergamon-elsevier Science Ltd en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.scopus.citedbyCount 8
dc.subject Hiv Mathematical Model en_US
dc.subject Sfd And Nsfd Schemes en_US
dc.subject Routh-Hurwitz Criterion en_US
dc.subject Lyapunov Function en_US
dc.subject Local And Global Stability en_US
dc.title The impact of standard and nonstandard finite difference schemes on HIV nonlinear dynamical model tr_TR
dc.title The Impact of Standard and Nonstandard Finite Difference Schemes on Hiv Nonlinear Dynamical Model en_US
dc.type Article en_US
dc.wos.citedbyCount 5
dspace.entity.type Publication
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relation.isOrgUnitOfPublication.latestForDiscovery 26a93bcf-09b3-4631-937a-fe838199f6a5

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