Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics
Abstract The aim of this work is to develop a novel explicit unconditionally positivity preserving finite difference (FD) scheme and an implicit positive FD scheme for the numerical solution of dengue epidemic reaction–diffusion model with incubation period of virus. The proposed schemes are uncondi...
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SpringerOpen
2020-05-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02622-z |
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doaj-a342545ad16b4e33a99d8224f3ba09c62020-11-25T03:36:43ZengSpringerOpenAdvances in Difference Equations1687-18472020-05-012020112210.1186/s13662-020-02622-zPositive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamicsNauman Ahmed0Muhammad Rafiq1Dumitru Baleanu2Ali Saleh Alshomrani3Muhammad Aziz-ur Rehman4Department of Mathematics, University of Management and TechnologyFaculty of Engineering, University of Central PunjabDepartment of Mathematics, Cankaya UniversityFaculty of Science, Department of Mathematics, King Abdulaziz UniversityDepartment of Mathematics, University of Management and TechnologyAbstract The aim of this work is to develop a novel explicit unconditionally positivity preserving finite difference (FD) scheme and an implicit positive FD scheme for the numerical solution of dengue epidemic reaction–diffusion model with incubation period of virus. The proposed schemes are unconditionally stable and preserve all the essential properties of the solution of the dengue reaction diffusion model. This proposed FD schemes are unconditionally dynamically consistent with positivity property and converge to the true equilibrium points of dengue epidemic reaction diffusion system. Comparison of the proposed scheme with the well-known existing techniques is also presented. The time efficiency of both the proposed schemes is also compared, with the two widely used techniques.http://link.springer.com/article/10.1186/s13662-020-02622-zStructure preserving methodsFinite difference schemesDengue modelDiffusion epidemic systemNumerical simulations |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nauman Ahmed Muhammad Rafiq Dumitru Baleanu Ali Saleh Alshomrani Muhammad Aziz-ur Rehman |
| spellingShingle |
Nauman Ahmed Muhammad Rafiq Dumitru Baleanu Ali Saleh Alshomrani Muhammad Aziz-ur Rehman Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics Advances in Difference Equations Structure preserving methods Finite difference schemes Dengue model Diffusion epidemic system Numerical simulations |
| author_facet |
Nauman Ahmed Muhammad Rafiq Dumitru Baleanu Ali Saleh Alshomrani Muhammad Aziz-ur Rehman |
| author_sort |
Nauman Ahmed |
| title |
Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics |
| title_short |
Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics |
| title_full |
Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics |
| title_fullStr |
Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics |
| title_full_unstemmed |
Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics |
| title_sort |
positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2020-05-01 |
| description |
Abstract The aim of this work is to develop a novel explicit unconditionally positivity preserving finite difference (FD) scheme and an implicit positive FD scheme for the numerical solution of dengue epidemic reaction–diffusion model with incubation period of virus. The proposed schemes are unconditionally stable and preserve all the essential properties of the solution of the dengue reaction diffusion model. This proposed FD schemes are unconditionally dynamically consistent with positivity property and converge to the true equilibrium points of dengue epidemic reaction diffusion system. Comparison of the proposed scheme with the well-known existing techniques is also presented. The time efficiency of both the proposed schemes is also compared, with the two widely used techniques. |
| topic |
Structure preserving methods Finite difference schemes Dengue model Diffusion epidemic system Numerical simulations |
| url |
http://link.springer.com/article/10.1186/s13662-020-02622-z |
| work_keys_str_mv |
AT naumanahmed positiveexplicitandimplicitcomputationaltechniquesforreactiondiffusionepidemicmodelofdenguediseasedynamics AT muhammadrafiq positiveexplicitandimplicitcomputationaltechniquesforreactiondiffusionepidemicmodelofdenguediseasedynamics AT dumitrubaleanu positiveexplicitandimplicitcomputationaltechniquesforreactiondiffusionepidemicmodelofdenguediseasedynamics AT alisalehalshomrani positiveexplicitandimplicitcomputationaltechniquesforreactiondiffusionepidemicmodelofdenguediseasedynamics AT muhammadazizurrehman positiveexplicitandimplicitcomputationaltechniquesforreactiondiffusionepidemicmodelofdenguediseasedynamics |
| _version_ |
1724548514722086912 |