Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study

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dc.authoridAhmed, Nauman/0000-0003-1742-585X
dc.authoridIqbal, Muhammad Sajid/0000-0001-6929-8093
dc.authoridde la Sen, manuel/0000-0001-9320-9433
dc.authoridRafiq, Muhammad/0000-0002-2165-3479
dc.contributor.authorShaikh, Tahira Sumbal
dc.contributor.authorAkgul, Ali
dc.contributor.authorRehman, Muhammad Aziz ur
dc.contributor.authorAhmed, Nauman
dc.contributor.authorIqbal, Muhammad Sajid
dc.contributor.authorShahid, Naveed
dc.contributor.authorRafiq, Muhammad
dc.date.accessioned2024-12-24T19:33:32Z
dc.date.available2024-12-24T19:33:32Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractIn this article, the transmission dynamical model of the deadly infectious disease namedEbola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan(now South Sudan) and was identified in 1976. The novelty of the model under discussion is theinclusion of advection and diffusion in each compartmental equation. The addition of these two termsmakes the model more general. Similar to a simple population dynamic system, the prescribed modelalso has two equilibrium points and an important threshold, known as the basic reproductive number.The current work comprises the existence and uniqueness of the solution, the numerical analysis ofthe model, and finally, the graphical simulations. In the section on the existence and uniqueness ofthe solutions, the optimal existence is assessed in a closed and convex subset of function space. Forthe numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate thesolution of the continuous mathematical model. The main reason for the adoption of this technique isdelineated in the form of the positivity of the state variables, which is necessary for any populationmodel. The positivity of the applied scheme is verified by the concept of M-matrices. Since thenumerical method gives a discrete system of difference equations corresponding to a continuoussystem, some other relevant properties are also needed to describe it. In this respect, the consistencyand stability of the designed technique are corroborated by using Taylor's series expansion and Von Neumann's stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so.
dc.description.sponsorshipBasque Government [IT1555-22, KK-2022/00090]; MCIN/AEI [PID2021-1235430B-C21/C22]
dc.description.sponsorshipBasque Government, Grants IT1555-22 and KK-2022/00090. MCIN/AEI 269.10.13039/501100011033, Grant PID2021-1235430B-C21/C22.
dc.identifier.doi10.3390/axioms12010079
dc.identifier.issn2075-1680
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85146748018
dc.identifier.scopusqualityN/A
dc.identifier.urihttps://doi.org/10.3390/axioms12010079
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8190
dc.identifier.volume12
dc.identifier.wosWOS:000916914300001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofAxioms
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectreaction
dc.subjectadvection
dc.subjectdiffusion
dc.subjectoptimal solution
dc.subjectexplicit estimates
dc.subjectauxiliary data
dc.subjectstructure preserving
dc.titleAnalysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study
dc.typeArticle

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