Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study
dc.contributor.author | Shaikh, Tahira Sumbal | |
dc.contributor.author | Akgül, Ali | |
dc.contributor.author | Rehman, Muhammad Aziz ur | |
dc.contributor.author | Ahmed, Nauman | |
dc.contributor.author | Iqbal, Muhammad Sajid | |
dc.contributor.author | Shahid, Naveed | |
dc.contributor.author | Rafiq, Muhammad | |
dc.contributor.author | De la Sen Parte, Manuel | |
dc.date.accessioned | 2023-01-24T16:32:09Z | |
dc.date.available | 2023-01-24T16:32:09Z | |
dc.date.issued | 2023-01-12 | |
dc.identifier.citation | Axioms 12(1) : (2023) // Article ID 79 | es_ES |
dc.identifier.issn | 2075-1680 | |
dc.identifier.uri | http://hdl.handle.net/10810/59452 | |
dc.description.abstract | In this article, the transmission dynamical model of the deadly infectious disease named Ebola 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 the inclusion of advection and diffusion in each compartmental equation. The addition of these two terms makes the model more general. Similar to a simple population dynamic system, the prescribed model also 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 of the model, and finally, the graphical simulations. In the section on the existence and uniqueness of the solutions, the optimal existence is assessed in a closed and convex subset of function space. For the numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate the solution of the continuous mathematical model. The main reason for the adoption of this technique is delineated in the form of the positivity of the state variables, which is necessary for any population model. The positivity of the applied scheme is verified by the concept of M-matrices. Since the numerical method gives a discrete system of difference equations corresponding to a continuous system, some other relevant properties are also needed to describe it. In this respect, the consistency and 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. | es_ES |
dc.description.sponsorship | Basque Government, Grants IT1555-22 and KK-2022/00090. MCIN/AEI 269.10.13039/501100011033, Grant PID2021-1235430B-C21/C22. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | MDPI | es_ES |
dc.relation | info:eu-repo/grantAgreement/MICINN/PID2021-1235430B-C21/C22 | es_ES |
dc.rights | info:eu-repo/semantics/openAccess | es_ES |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | reaction | es_ES |
dc.subject | advection | es_ES |
dc.subject | diffusion | es_ES |
dc.subject | optimal solution | es_ES |
dc.subject | explicit estimates | es_ES |
dc.subject | auxiliary data | es_ES |
dc.subject | structure preserving | es_ES |
dc.title | Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.date.updated | 2023-01-20T14:22:47Z | |
dc.rights.holder | © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/). | es_ES |
dc.relation.publisherversion | https://www.mdpi.com/2075-1680/12/1/79 | es_ES |
dc.identifier.doi | 10.3390/axioms12010079 | |
dc.departamentoes | Electricidad y electrónica | |
dc.departamentoeu | Elektrizitatea eta elektronika |
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Except where otherwise noted, this item's license is described as © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/).