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Design, analysis and comparison of a nonstandard computational method for the solution of a general stochastic fractional epidemic model

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dc.contributor.author Ahmed, Nauman
dc.contributor.author Macías-Díaz, Jorge E.
dc.contributor.author Raza, Ali
dc.contributor.author Iqbal, Zafar
dc.contributor.author Ahmad, Muhammad Ozair
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Rafiq, Muhammad
dc.date.accessioned 2024-03-04T11:15:27Z
dc.date.available 2024-03-04T11:15:27Z
dc.date.issued 2022-01
dc.identifier.citation 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. tr_TR
dc.identifier.issn 20751680
dc.identifier.uri http://hdl.handle.net/20.500.12416/7460
dc.description.abstract 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. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.3390/axioms11010010 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Boundedness tr_TR
dc.subject Malaria Infection tr_TR
dc.subject Nonstandard Finite-Difference Method tr_TR
dc.subject Positivity tr_TR
dc.subject Stochastic Epidemic Model tr_TR
dc.subject Stochastic Generalized Euler tr_TR
dc.title Design, analysis and comparison of a nonstandard computational method for the solution of a general stochastic fractional epidemic model tr_TR
dc.type article tr_TR
dc.relation.journal Axioms tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 11 tr_TR
dc.identifier.issue 1 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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