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

dc.contributor.authorBukhsh, Imam
dc.contributor.authorAsjad, Muhammad Imran
dc.contributor.authorEldin, Sayed M.
dc.contributor.authorEl-Rahman, Magda Abd
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorLi, Shuo
dc.contributor.authorID56389tr_TR
dc.date.accessioned2024-01-24T11:54:22Z
dc.date.available2024-01-24T11:54:22Z
dc.date.issued2023
dc.departmentÇankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractMathematical models are enormously valuable in recognition the characteristics of infectious afflictions. The present study describes and analyses a nonlinear Susceptible-Infected (S·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.publishedMonth8
dc.identifier.citationLi, 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.doi10.1016/j.chaos.2023.113755
dc.identifier.issn9600779
dc.identifier.urihttp://hdl.handle.net/20.500.12416/6964
dc.identifier.volume173en_US
dc.language.isoenen_US
dc.relation.ispartofChaos, Solitons and Fractalsen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectHIV Mathematical Modelen_US
dc.subjectLocal And Global Stabilityen_US
dc.subjectSFD And NSFD Schemesen_US
dc.subjectLyapunov Functionen_US
dc.subjectLyapunov Functionen_US
dc.titleThe impact of standard and nonstandard finite difference schemes on HIV nonlinear dynamical modeltr_TR
dc.titleThe Impact of Standard and Nonstandard Finite Difference Schemes on Hiv Nonlinear Dynamical Modelen_US
dc.typeArticleen_US
dspace.entity.typePublication

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